If a linear equation has solutions (-2, 2), (0, 0) and (2, – 2), then it is of the form. -Maths 9th

If a linear equation has solutions (-2, 2), (0, 0) and (2, – 2), then it is of the form. -Maths 9th
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Answer :

(b) Let us consider a linear equation ax + by + c = 0 … (i) Since, (-2,2), (0, 0) and (2, -2) are the solutions of linear equation therefore it satisfies the Eq. (i), we get At point(-2,2), -2a + 2b + c = 0 …(ii) At point (0, 0), 0+0 + c = 0 ⇒ c = 0 …(iii) and at point (2, – 2), 2a-2b + c = 0 …(iv) From Eqs. (ii) and (iii), c = 0 and – 2a + 2b + 0 = 0, – 2a = -2b,a = 2b/2 ⇒a = b On putting a = b and c = 0 in Eq. (i), bx + by + 0= 0 ⇒ bx + by = 0 ⇒ – b(x + y)= 0 ⇒ x + y = 0, b ≠ 0 Hence, x + y= 0 is the required form of the linear equation.
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Related questions

If a linear equation has solutions (-2, 2), (0, 0) and (2, – 2), then it is of the form. -Maths 9th

Description : If a linear equation has solutions (-2, 2), (0, 0) and (2, – 2), then it is of the form. -Maths 9th

Last Answer : (b) Let us consider a linear equation ax + by + c = 0 (i) Since, (-2,2), (0, 0) and (2, -2) are the solutions of linear equation therefore it satisfies the Eq. (i), we get At point(-2,2), -2a + 2b + c ... b(x + y)= 0 ⇒ x + y = 0, b ≠ 0 Hence, x + y= 0 is the required form of the linear equation.

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Last Answer : Given equation is 4x + 3y =12 On putting x = 0 in Eq. (i), we get 4(0) +3y =12 ⇒ 3y =12 ⇒ y = 12 / 3 = 4 So, (0, 4) is a solution of given equation. On putting y = 0 in Eq. (i), we ... given equation. Hence the four solutions of given equation are (0, 4), (3, 0), (1, 8 / 3) and (2,4 / 3).

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Description : How many solutions of the equation 2x + 1 = x – 3 are there on the Cartesian plane? -Maths 9th

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Description : Find any four solutions of the equation 4x+3y=12. -Maths 9th

Last Answer : Given equation is 4x + 3y =12 On putting x = 0 in Eq. (i), we get 4(0) +3y =12 ⇒ 3y =12 ⇒ y = 12 / 3 = 4 So, (0, 4) is a solution of given equation. On putting y = 0 in Eq. (i), we ... given equation. Hence the four solutions of given equation are (0, 4), (3, 0), (1, 8 / 3) and (2,4 / 3).

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Description : How many solutions of the equation 2x + 1 = x – 3 are there on the Cartesian plane? -Maths 9th

Last Answer : 2x + 1 = x - 3 2x-x = -3-1 ∴ x = - 4 ..(i) and it can be written as 1.x + 0. y = - 4 ..(ii) (i) Number line represent the all real values of x on the X ... the equation x + 4 = 0 represent a straight line parallel to Y-axis and infinitely many points lie on a line in the cartesian plane.

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Description : How many solutions does the equation 2x +5y=8 has? -Maths 9th

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Description : Write two solutions of the equation 4x -5 y = 15. -Maths 9th

Last Answer : Solution :-

The number of solutions satisfying the given equation -Maths 9th

Description : The number of solutions satisfying the given equation -Maths 9th

Last Answer : (d) 3Taking log of both the sides to base 3, we have,\(\big[(log_3\,x)^2-rac{9}{2}log_3\,x+5\big]\) log3x = log333/2 = \(rac{3}{2}\) (∵ log33 = 1)⇒ 2(log3x)3 - 9(log3x)2 + 10 log3x - 3 = 0 ⇒ ... log3x = 3, 2 log3x = 1 ⇒ x = 31, x = 33, x2 = 31⇒ \(x\) = (3, 27, √3)∴ There are three solutions.

What are the number of solutions for real x, which satisfy the equation -Maths 9th

Description : What are the number of solutions for real x, which satisfy the equation -Maths 9th

Last Answer : log2 x>0 2log2 log2 x+log21 log2 (22 x)=1 ⇒2log2 log2 x−log2 log2 (22 x)=1[∵loga1 b=−loga b] $$\Rightarrow \log _{ 2 }{ \left[ \dfrac { { \left( \log _{ 2 }{ x } \right) }^{ 2 } }{ \log_{ 2 } ... log2 (22 )2=log2 8=log2 23=3] ⇒t=3,−1=log2 x ⇒x=2−1or 23 That is x=21 or 8 Hence, the answer is 8.

What is the general form of linear equation in two variables ? -Maths 9th

Description : What is the general form of linear equation in two variables ? -Maths 9th

Last Answer : The general form of linear equation in two variables can be written as: ax+by+c=0

Express the given statement in the form of a linear equation in two variables. The sum of the ordinate and abscissa of a point is 6. -Maths 9th

Description : Express the given statement in the form of a linear equation in two variables. The sum of the ordinate and abscissa of a point is 6. -Maths 9th

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Express the given equation as linear equation in two variables in standard form: 3y = 2x. -Maths 9th

Description : Express the given equation as linear equation in two variables in standard form: 3y = 2x. -Maths 9th

Last Answer : Solution :- 2x - √3y + 0 = 0

Let cost of a pen and a pencil be “x” and “y” respectively. A girl pays ₹16 for 2 pens and 3 pencils. Write the given data in the form of a linear equation in two variables. Also represent it graphically. -Maths 9th

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Last Answer : Solution :-

The work done by a body on application of a constant force is the product of the constant force and distance travelled by the body in the direction of force. Express this in the form of a linear equation in two variables and draw its graph by taking the constant force as 3 units. -Maths 9th

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On planet A , each alien has 3 eyes and on planet B , each alien has 4 eyes. A group of aliens from planets A and B landed on earth. They had 30 eyes in all. Assuming number of aliens from planets A and B respectively , express the situation in the form of linear equation in two variables. -Maths 9th

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Twice the number of marbles with Aman exceeds thrice the number of marbles with Vinay by 12. Assume the number of marbles with Aman and Vinay as x and y respectively .Express the statement in the form of a linear equation in two variables. -Maths 9th

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Five years hence , the age of Ram will be 10 more than the two thirds of Ravi’s age . Assume the present ages of Ram and Ravi as x and y respectively . Express the statement in the form of a linear equation in two variables. -Maths 9th

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The ordinate of a point is thrice its abscissa. Express the statement in the form of a linear equation in two variables. -Maths 9th

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The linear equation 2x – 5y = 7 has -Maths 9th

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The graph of the linear equation 2x + 3y = 6 cuts the Y-axis at the point. -Maths 9th

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Last Answer : (d) Since, the graph of linear equation 2x + 3y = 6 cuts the Y-axis. So, we put x = 0 in the given equation 2x+ 3y = 6, we get 2 x 0+ 3y = 6 ⇒ 3y = 6 y = 2. Hence, at the point (0, 2), the given linear equation cuts the Y-axis.

x = 5 and y = 2 is a solution of the linear equation. -Maths 9th

Description : x = 5 and y = 2 is a solution of the linear equation. -Maths 9th

Last Answer : (c) (a) Take x + 2y, on putting x=5 and y = 2, we get 5 + 2(2) = 5+ 4 = 9≠7. So, (5, 2) is not a solution of x + 2y = 7 (b) Take 5x + 2y, on putting x = 5 and y = 2, we get 5x 5 + 2 x2 =25+ 4 = ... on putting x = 5 and y = 2, we get 5 5 + 2=25 + 2 =27 ≠7 So, (5, 2) is not a solution of 5x + y = 7.

The graph of the linear equation 2x+ 3y = 6 is a line which meets the X-axis at the point. -Maths 9th

Description : The graph of the linear equation 2x+ 3y = 6 is a line which meets the X-axis at the point. -Maths 9th

Last Answer : (c) Since, the graph of linear equation 2x + 3y = 6 meets the X-axis. So, we put y = 0 in 2x + 3y = 6 ⇒ 2x + 3(0) = 6 = 2x + 0 = 6 ⇒ x = 6/2 ⇒ x = 3 Hence, the coordinate on X-axis is (3, 0).