Chapter 3 Pair of Linear Equations in Two Variables

Chapter 3 Pair of Linear Equations in Two Variables
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Chapter 3 Pair of Linear Equations in Two Variables

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Chapter 3 Pair of Linear Equations in Two Variables

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Chapter 3 Pair of Linear Equations in Two Variables

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Chapter 3 Pair of Linear Equations in Two Variables

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In the following figure ABCD is a cyclic quadrilateral, the sum of degree measures of ∠A and ∠D is: (SOURCE: Fig. 3.7, Exercise 3.7, Chapter 3, PAIR of LINEAR EQUATIONS in TWO VARIABLES, NCERT, Class X) (a) 120° (b) 180° (c) 230°(d) 250°

Description : In the following figure ABCD is a cyclic quadrilateral, the sum of degree measures of ∠A and ∠D is: (SOURCE: Fig. 3.7, Exercise 3.7, Chapter 3, PAIR of LINEAR EQUATIONS in TWO VARIABLES, NCERT, Class X) (a) 120° (b) 180° (c) 230°(d) 250°

Last Answer : (c) 230°

Out of the following linear equations in two variables, the two representing a pair of parallel lines graphically are: 3x - 4y = 6 3x + 4y = 6 6x + 8y = 12 6x - 8y + 6 = 0 (a) 3x - 4y = 6 and 6x + 8y = 12 (b) 3x - 4y = 6 and 6x - 8y + 6 = 0 (c) 6x + 8y = 12 and 3x + 4y = 6 (d) 6x - 8y + 6 = 0 and 3x + 4y = 6

Description : Out of the following linear equations in two variables, the two representing a pair of parallel lines graphically are: 3x - 4y = 6 3x + 4y = 6 6x + 8y = 12 6x - 8y + 6 = 0 (a) 3x - 4y = 6 and 6x + 8y = 12 (b) 3x - 4y = 6 ... 6 = 0 (c) 6x + 8y = 12 and 3x + 4y = 6 (d) 6x - 8y + 6 = 0 and 3x + 4y = 6

Last Answer : (b) 3x - 4y = 6 and 6x - 8y + 6 = 0

If (x, y) is a solution of the following pair of linear equations in two variables, then the value of expression (√ is: x + 2y = 4 and 3x - y = 5 (a) 2 (b) 3 (c) 4 (d) √

Description : If (x, y) is a solution of the following pair of linear equations in two variables, then the value of expression (√ is: x + 2y = 4 and 3x - y = 5 (a) 2 (b) 3 (c) 4 (d) √2

Last Answer : (a) 2

The solution of the following system of linear equations in two variables is: 55x + 67y = 311; 67x + 55y = 299 (a) (2, 3) (b) (3, 2) (c) (-2,3) (d) (3, -2)

Description : The solution of the following system of linear equations in two variables is: 55x + 67y = 311; 67x + 55y = 299 (a) (2, 3) (b) (3, 2) (c) (-2,3) (d) (3, -2)

Last Answer : (b) (3, 2)

Which of the following pair of linear equations represent the two parallel tracks of the railway line? a) x-2y-4=0 and 2x + 4y - 12 = 0 c) 2x + 4y -12 = 0 and x +2y-4=0 b) x +2y-4=0 and 2x + 4y +12 = 0 d) 2x + 4y + 12 = 0 and x-2y-4=0

Description : Which of the following pair of linear equations represent the two parallel tracks of the railway line? a) x-2y-4=0 and 2x + 4y - 12 = 0 c) 2x + 4y -12 = 0 and x +2y-4=0 b) x +2y-4=0 and 2x + 4y +12 = 0 d) 2x + 4y + 12 = 0 and x-2y-4=0

Last Answer : c) 2x + 4y -12 = 0 and x +2y-4=0

What is the value of x, y in the following pair of linear equations: 4x + = 15 , 6x – = 14 ? (a) 3,2 (b) -3,-2 (c) 3,-2 (d) -3,2

Description : What is the value of x, y in the following pair of linear equations: 4x + = 15 , 6x – = 14 ? (a) 3,2 (b) -3,-2 (c) 3,-2 (d) -3,2

Last Answer : (a) 3,2

What is the value of x, y in the following pair of linear equations: 4x + = 15 , 6x – = 14 ? (a) 3,2 (b) -3,-2 (c) 3,-2 (d) -3,2

Description : What is the value of x, y in the following pair of linear equations: 4x + = 15 , 6x – = 14 ? (a) 3,2 (b) -3,-2 (c) 3,-2 (d) -3,2

Last Answer : (a) 3,2

Assertion (A):A pair of linear equations has no solution (s) if it represented by intersecting lines graphically. Reason (R) : If the pair of lines are intersecting, then the pair has unique solution and is called consistent pair of equations. (a) Both A and R are correct; R is the correct explanation of A. (b) Both A and R are correct; R is not the correct explanation of A. (c) A is correct; R is incorrect. (d) R is correct; A is incorrect.

Description : Assertion (A):A pair of linear equations has no solution (s) if it represented by intersecting lines graphically. Reason (R) : If the pair of lines are intersecting, then the pair has unique solution and is called ... of A. (c) A is correct; R is incorrect. (d) R is correct; A is incorrect.

Last Answer : (d) R is correct; A is incorrect.

The value(s) of 'k' for which the following pair of linear equations will represent a pair of intersecting lines graphically is/are: 3x - 4y + 7 = 0 kx - 8y = 5 (a) k = 6 (b) k ≠ 6(c) any real number (d) any real number except 6

Description : The value(s) of 'k' for which the following pair of linear equations will represent a pair of intersecting lines graphically is/are: 3x - 4y + 7 = 0 kx - 8y = 5 (a) k = 6 (b) k ≠ 6(c) any real number (d) any real number except 6

Last Answer : (d) any real number except 6

"Ravi is 10 years older than Rehan. Five years ago, one-seventh of Ravi's age was equal to one-fifth of Rehan's age." If Rehan's age be 'x' years and Ravi's age be 'y' years, which of the following pair of linear equations is describing it algebraically? (a) x - y = 10 and 7x - 5y + 10 = 0 (b) y -x = 10 and 5y -7x + 10 = 0 (c) x + y = 10 and 7x + 5y - 10 = 0 (d) x - y = -10 and 7y - 5x + 10 = 0

Description : "Ravi is 10 years older than Rehan. Five years ago, one-seventh of Ravi's age was equal to one-fifth of Rehan's age." If Rehan's age be 'x' years and Ravi's age be 'y' years, which of the following pair of linear equations is ... y = 10 and 7x + 5y - 10 = 0 (d) x - y = -10 and 7y - 5x + 10 = 0

Last Answer : (b) y -x = 10 and 5y -7x + 10 = 0

A pair of linear equations which has a unique solution x = 2, y = -3 is (a) x + y = -1 ; 2x – 3y = -5 (b) 2x + 5y = -11 ; 4x + 10y = -22(c) 2x – y = 1 ; 3x + 2y = 0 (d) x – 4y – 14 = 0 ;5x – y – 13 = 0

Description : A pair of linear equations which has a unique solution x = 2, y = -3 is (a) x + y = -1 ; 2x – 3y = -5 (b) 2x + 5y = -11 ; 4x + 10y = -22(c) 2x – y = 1 ; 3x + 2y = 0 (d) x – 4y – 14 = 0 ;5x – y – 13 = 0

Last Answer : (d) x – 4y – 14 = 0 ;5x – y – 13 = 0

One equation of a pair of dependent linear equations is -5x+7y=2 .The second equation can be (a)10x-14y-4=0 (b) -10x+14y+4=0 (c) 10x-14y-4=0 (d) -10x+14y-4=0

Description : One equation of a pair of dependent linear equations is -5x+7y=2 .The second equation can be (a)10x-14y-4=0 (b) -10x+14y+4=0 (c) 10x-14y-4=0 (d) -10x+14y-4=0

Last Answer : (d) -10x+14y-4=0

MCQ Questions for Class 9 Maths Chapter 4 Linear Equations in Two Variables with answers -Maths 9th

Description : MCQ Questions for Class 9 Maths Chapter 4 Linear Equations in Two Variables with answers -Maths 9th

Last Answer : 1) The linear equation 3x-11y=10 has: a. Unique solution b. Two solutions c. Infinitely many solutions d.No solutions c Explanation: 3x-11y=10 y=(3x-10)/11 Now for infinite values of x, y will ... c=0, always lie in the: a. First quadrant b. Second quadrant c. Third quadrant d. Fourth quadrant a

Cbqs (case base study ) of chapter 4 Linear Equations in Two Variables of maths class 9th -Maths 9th

Description : Cbqs (case base study ) of chapter 4 Linear Equations in Two Variables of maths class 9th -Maths 9th

Last Answer : answer:

Chapter 4 Quadratic Equations

Description : Chapter 4 Quadratic Equations

Last Answer : Chapter 4 Quadratic Equations

If lines corresponding to given linear equations are coincident, the solutionof the given equations is: e) Unique solution f) Two solutionsg) Infintely many solutions h) No solution

Description : If lines corresponding to given linear equations are coincident, the solutionof the given equations is: e) Unique solution f) Two solutionsg) Infintely many solutions h) No solution

Last Answer : g) Infintely many solutions

If lines corresponding to given linear equations are coincident, the solutionof the given equations is: a) Unique solution b) Two solutions c) Infintely many solutions d) No solution

Description : If lines corresponding to given linear equations are coincident, the solutionof the given equations is: a) Unique solution b) Two solutions c) Infintely many solutions d) No solution

Last Answer : c) Infintely many solutions

What are some fast ways to solve a system of 3 linear equations with this special form?

Description : What are some fast ways to solve a system of 3 linear equations with this special form?

Last Answer : Perhaps an algebraic matrix ?

Assertion (A) : The value of k for which the system of linear equations kx+2y+1=0 and 6x+4y-5=0 has a unique solution is 3. Reason (R):The system of linear equations a1x + b1y + c1= 0 and a2x + b2y + c2 = 0 has a unique solution if (a) Both A and R are correct; R is the correct explanation of A. (b) Both A and R are correct; R is not the correct explanation of A. (c) A is correct; R is incorrect. (d) R is correct; A is incorrect.

Description : Assertion (A) : The value of k for which the system of linear equations kx+2y+1=0 and 6x+4y-5=0 has a unique solution is 3. Reason (R):The system of linear equations a1x + b1y + c1= 0 and a2x + ... not the correct explanation of A. (c) A is correct; R is incorrect. (d) R is correct; A is incorrect.

Last Answer : (d) R is correct; A is incorrect.

The pair of equations y=0 and y=-7 has (a)one solution (b)two solutions (c)no solution (d)infinitely many solutions

Description : The pair of equations y=0 and y=-7 has (a)one solution (b)two solutions (c)no solution (d)infinitely many solutions

Last Answer : (c)no solution

The pair of equations 3 x + y = 81 , 81 x – y = 3 has (a) no solution (b) unique solution (c) infinitely many solutions (d) x = 2 , y = 1

Description : The pair of equations 3 x + y = 81 , 81 x – y = 3 has (a) no solution (b) unique solution (c) infinitely many solutions (d) x = 2 , y = 1

Last Answer : d) x = 2 , y = 1

The pair of equations 3 x + y = 81 , 81 x – y = 3 has (a) no solution (b) unique solution (c) infinitely many solutions (d) x = 2 , y = 1

Description : The pair of equations 3 x + y = 81 , 81 x – y = 3 has (a) no solution (b) unique solution (c) infinitely many solutions (d) x = 2 , y = 1

Last Answer : d) x = 2 , y = 1

The pair of equations ax+by+c=0 and dx+ey+c=0 represent the equations with infinitely many solutions if (a)ad=be (b)ae=bd (c)ab=de (d)ac=de

Description : The pair of equations ax+by+c=0 and dx+ey+c=0 represent the equations with infinitely many solutions if (a)ad=be (b)ae=bd (c)ab=de (d)ac=de

Last Answer : (b)ae=bd

The pair of equations ax+2y=7 and 3x+by=16 represent parallel lines if (a)a=b (b)3a=2b (c)ab=6 (d)2a=3b

Description : The pair of equations ax+2y=7 and 3x+by=16 represent parallel lines if (a)a=b (b)3a=2b (c)ab=6 (d)2a=3b

Last Answer : (c)ab=6

One equation of a pair of dependent linear equation is -2x + 3y = 9 , the second equation can be e) 4x + 6y = 18 f) 4x - 6y = - 18 g) -4x – 6y = 18 h) None of these

Description : One equation of a pair of dependent linear equation is -2x + 3y = 9 , the second equation can be e) 4x + 6y = 18 f) 4x - 6y = - 18 g) -4x – 6y = 18 h) None of these

Last Answer : f) 4x - 6y = - 18

One equation of a pair of dependent linear equation is -2x + 3y = 9 , the second equation can be a) 4x + 6y = 18 b) 4x - 6y = - 18 c) -4x – 6y = 18 d) None of these

Description : One equation of a pair of dependent linear equation is -2x + 3y = 9 , the second equation can be a) 4x + 6y = 18 b) 4x - 6y = - 18 c) -4x – 6y = 18 d) None of these

Last Answer : b) 4x - 6y = - 18

Linear Equations in Two Variables Class 9th Formulas -Maths 9th

Description : Linear Equations in Two Variables Class 9th Formulas -Maths 9th

Last Answer : Rational Numbers : Rational Numbers are numbers , which can be expressed in the form p/q, q≠0; where p and q are integers . The collection of all rationals are represented by Q. ∴ Q = {p/q ; p,q ... number of rational numbers x2 , x1, x3,... between any two rational numbers a and b so that a

Is this statement true or falseA system of linear equations is a set of two or more equations with the same variables, and the graph of each equation is a line?

Description : Is this statement true or falseA system of linear equations is a set of two or more equations with the same variables, and the graph of each equation is a line?

Last Answer : 1

is a statistical technique which determines and quantifies the relationship between variables and enables standard equations to be established for energy consumption. a) linear regression analysis b) time-dependent energy analysis c) moving annual total d) CUSUM

Description : is a statistical technique which determines and quantifies the relationship between variables and enables standard equations to be established for energy consumption. a) linear regression analysis b) time-dependent energy analysis c) moving annual total d) CUSUM

Last Answer : a) linear regression analysis

Why don't these two identical math equations equal the same thing? (See picture.)

Description : Why don't these two identical math equations equal the same thing? (See picture.)

Last Answer : Once the gif started cutting the boxes into pieces, it’s all optical illusion. they changed the number of boxes in the rectangle with that little geometric magic.

The ratio of the areas of the two triangles formed by the lines representing the equations and 2x – y + 2 = 0 with X axis and the lines with the Y axis is (a) 1 : 2 (b) 2 : 1 (c) 4 : 1 (d) 1 : 4

Description : The ratio of the areas of the two triangles formed by the lines representing the equations and 2x – y + 2 = 0 with X axis and the lines with the Y axis is (a) 1 : 2 (b) 2 : 1 (c) 4 : 1 (d) 1 : 4

Last Answer : (c) 4 : 1

. The ratio of the areas of the two triangles formed by the lines representing the equations and 2x – y + 2 = 0 with X axis and the lines with the Y axis is (a) 1 : 2 (b) 2 : 1 (c) 4 : 1 (d) 1 : 4

Description : . The ratio of the areas of the two triangles formed by the lines representing the equations and 2x – y + 2 = 0 with X axis and the lines with the Y axis is (a) 1 : 2 (b) 2 : 1 (c) 4 : 1 (d) 1 : 4

Last Answer : (c) 4 : 1

How do I find the amount of possible equations for a certain number?

Description : How do I find the amount of possible equations for a certain number?

Last Answer : Infinity is all the combinations

If = = in the system of equations a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0 Statement 1 : This is the condition for inconsistent equations Statement 2 : There exists infinitely many solutions Statement 3 : The equations satisfying the condition are parallel Which of the above statements are true ? e) S1 only f) S1 and S2 g) S1 and S3 h) S2 only Answer: (d) S2 o

Description : If = = in the system of equations a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0 Statement 1 : This is the condition for inconsistent equations Statement 2 : There exists infinitely many solutions ... statements are true ? e) S1 only f) S1 and S2 g) S1 and S3 h) S2 only Answer: (d) S2 o

Last Answer : h) S2 only

The value of x and y which satisfy the equations : √ e) x=1,y=0 f) x=0,y=0 g) x=1,y=1 h) x=0,y=1

Description : The value of x and y which satisfy the equations : √ e) x=1,y=0 f) x=0,y=0 g) x=1,y=1 h) x=0,y=1

Last Answer : f) x=0,y=0

The value of m obtained on solving equations : 2n + m =2n – m = √ a) 1/4 b) 0 c) 1/2 d) 3/4

Description : The value of m obtained on solving equations : 2n + m =2n – m = √ a) 1/4 b) 0 c) 1/2 d) 3/4

Last Answer : b) 0

For what value of k , the following system of equations have infinite solutions : kx + 4y = k-4, 16x + ky = k (a) k = 2 (b) k = 4 (c) k = 6 (d) k = 8

Description : For what value of k , the following system of equations have infinite solutions : kx + 4y = k-4, 16x + ky = k (a) k = 2 (b) k = 4 (c) k = 6 (d) k = 8

Last Answer : (d) k = 8

If = = in the system of equations a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0 Statement 1 : This is the condition for inconsistent equations Statement 2 : There exists infinitely many solutions Statement 3 : The equations satisfying the condition are parallel Which of the above statements are true ? a) S1 only b) S1 and S2 c) S1 and S3 d) S2 only

Description : If = = in the system of equations a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0 Statement 1 : This is the condition for inconsistent equations Statement 2 : There exists infinitely many ... parallel Which of the above statements are true ? a) S1 only b) S1 and S2 c) S1 and S3 d) S2 only

Last Answer : d) S2 only

The value of x and y which satisfy the equations : √ a) x=1,y=0 b) x=0,y=0 c) x=1,y=1 d) x=0,y=1

Description : The value of x and y which satisfy the equations : √ a) x=1,y=0 b) x=0,y=0 c) x=1,y=1 d) x=0,y=1

Last Answer : b) x=0,y=0

The value of m obtained on solving equations : 2n + m =2n – m = √ a) 1/4 b) 0 c) 1/2 d) 3/4

Description : The value of m obtained on solving equations : 2n + m =2n – m = √ a) 1/4 b) 0 c) 1/2 d) 3/4

Last Answer : b) 0

For what value of k , the following system of equations have infinite solutions : kx + 4y = k-4, 16x + ky = k (a) k = 2 (b) k = 4 (c) k = 6 (d) k = 8

Description : For what value of k , the following system of equations have infinite solutions : kx + 4y = k-4, 16x + ky = k (a) k = 2 (b) k = 4 (c) k = 6 (d) k = 8

Last Answer : (d) k = 8

NCERT Solutions for class 9 Maths Chapter 4 Linear Equation in Two Variables Exercise 4.1 -Maths 9th

Description : NCERT Solutions for class 9 Maths Chapter 4 Linear Equation in Two Variables Exercise 4.1 -Maths 9th

Last Answer : (i) (x + 4)(x + 10): Using the identity (x + a)(x + b) = x2 + (a + b)x + ab, we have: (x + 4)(x + 10) = x2 + (4 + 10)x + (4 x 10) = x2 + 14x + 40 (ii) (x + 8)(x - 10): Here, a = 8 and b = ( ... have 64m3 - 343n3 = (4m)3 - (7n)3 = (4m - 7n)[(4m)2 + (4m)(7n) + (7n)2] = (4m - 7n)(16m2 + 28mn + 49n2)

NCERT Solutions for class 9 Maths Chapter 4 Linear Equation in Two Variables Exercise 4.2 -Maths 9th

Description : NCERT Solutions for class 9 Maths Chapter 4 Linear Equation in Two Variables Exercise 4.2 -Maths 9th

Last Answer : 1. How will you describe the position of a table lamp on your study table to another person ? To describe the position of a table lamp placed on the table, let us consider the table lamp as P and the table as a plane ... the point A(4, 3). (ii) A unique cross street as shown by the point B(3, 4).

NCERT Solutions for class 9 Maths Chapter 4 Linear Equation in Two Variables Exercise 4.3 -Maths 9th

Description : NCERT Solutions for class 9 Maths Chapter 4 Linear Equation in Two Variables Exercise 4.3 -Maths 9th

Last Answer : 1: Draw the graph of each of the following linear equations in two variables: (i) x + y = 4 (ii) x - y = 2 (iii) y = 3x (iv) 3 = 2x + y Solution: (i)x + y= 4 ⇒ y = 4 - x If ... graph paper and joining them, we get a straight line PQ. Thus, PQ is the required graph of the linear equation y = 5x + 3.

NCERT Solutions for class 9 Maths Chapter 4 Linear Equation in Two Variables Exercise 4.4 -Maths 9th

Description : NCERT Solutions for class 9 Maths Chapter 4 Linear Equation in Two Variables Exercise 4.4 -Maths 9th

Last Answer : 1. Give the geometric representations of y = 3 as an equation (i) in one variable (ii) in two variables (i) y = 3 [An equation in one variable] ∵ y = 3 is an equation in one variable, i.e. y only. ∴ It has ... equation in two variables] We can write 2x + 9 = 0 as 2x + 0y + 9 = 0 or 2x = -9 + 0y

Chapter 15 Probability

Description : Chapter 15 Probability

Last Answer : Chapter 15 Probability

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Description : Chapter 14 Statistics

Last Answer : Chapter 14 Statistics

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Description : Chapter 13 Surface Areas and Volumes

Last Answer : Chapter 13 Surface Areas and Volumes

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Description : Chapter 12 Areas Related to Circles

Last Answer : Chapter 12 Areas Related to Circles

Chapter 11 Constructions

Description : Chapter 11 Constructions

Last Answer : Chapter 11 Constructions