Solve the following equations for x and y. log100 |x+y| = 1/2, -Maths 9th

Solve the following equations for x and y. log100 |x+y| = 1/2, -Maths 9th
by

1 Answer

Answer :

(b) \(\bigg(rac{10}{3},rac{20}{3}\bigg)\). (+ 10, 20) log100 |x+y| = \(rac{1}{2}\) ⇒ |x + y| = 100\(^{rac{1}{2}}\)⇒ |x + y| = 10 as (–10 is inadmissible)        ...(i) log10y – log10| x | = log1004⇒ log10 \(rac{y}{|x|}\) = log102 = log10 2         \(\big[\)Using logan (xm) = \(rac{m}{n}\) loga x\(\big]\)⇒ \(rac{y}{|x|}\) = 2 ⇒ y = 2 | x |                            ...(ii)Substituting the value of y from (ii) in (i), we get | x + 2| x || = 10 If x > 0, then 3x = 10 ⇒ x = \(rac{10}{3}\)If x < 0, then x = 10.∴ If x = \(rac{10}{3}\), then y = \(rac{20}{3}\) and if x = 10, y = 20.
by

Related questions

Solve these following equations: (i) 3x + 3 = 15 (ii) 2y + 7 =19 -Maths 9th

Description : Solve these following equations: (i) 3x + 3 = 15 (ii) 2y + 7 =19 -Maths 9th

Last Answer : answer:

In the following equations , find which of the variables x, y, z etc. represent rational numbers and which represent irrational numbers -Maths 9th

Description : In the following equations , find which of the variables x, y, z etc. represent rational numbers and which represent irrational numbers -Maths 9th

Last Answer : Following are the rational numbers which represent irrational numbers .

How many linear equations in x and y can be satisfied by x = 1 and y = 2 ? -Maths 9th

Description : How many linear equations in x and y can be satisfied by x = 1 and y = 2 ? -Maths 9th

Last Answer : (c) Let the linear equation be ax + by + c = 0. On putting x = 1 and y = 2, in above equation we get =s a + 2b + c = 0, where a, b and c, are real number Here, different values of a, b and ... a + 2b + c = 0. Hence, infinitely many linear equations in x and yean be satisfied by x = 1 and y = 2.

Draw the graphs of linear equations y = x and y = – x on the same Cartesian plane. -Maths 9th

Description : Draw the graphs of linear equations y = x and y = – x on the same Cartesian plane. -Maths 9th

Last Answer : The given equation is y = x. To draw the graph of this equations, we need atleast two points lying on the given line. For x = 1, y = 1, therefore (1,1) satisfies the linear equation y = x. For x = 4, y = 4, ... of y = - x. We observe that, the line y = x and y = - x intersect at the point 0(0, 0).

In the following equations , find which of the variables x, y, z etc. represent rational numbers and which represent irrational numbers -Maths 9th

Description : In the following equations , find which of the variables x, y, z etc. represent rational numbers and which represent irrational numbers -Maths 9th

Last Answer : Following are the rational numbers which represent irrational numbers .

How many linear equations in x and y can be satisfied by x = 1 and y = 2 ? -Maths 9th

Description : How many linear equations in x and y can be satisfied by x = 1 and y = 2 ? -Maths 9th

Last Answer : (c) Let the linear equation be ax + by + c = 0. On putting x = 1 and y = 2, in above equation we get =s a + 2b + c = 0, where a, b and c, are real number Here, different values of a, b and ... a + 2b + c = 0. Hence, infinitely many linear equations in x and yean be satisfied by x = 1 and y = 2.

Draw the graphs of linear equations y = x and y = – x on the same Cartesian plane. -Maths 9th

Description : Draw the graphs of linear equations y = x and y = – x on the same Cartesian plane. -Maths 9th

Last Answer : The given equation is y = x. To draw the graph of this equations, we need atleast two points lying on the given line. For x = 1, y = 1, therefore (1,1) satisfies the linear equation y = x. For x = 4, y = 4, ... of y = - x. We observe that, the line y = x and y = - x intersect at the point 0(0, 0).

How many linear equations satisfy x = 2 and y = -3? -Maths 9th

Description : How many linear equations satisfy x = 2 and y = -3? -Maths 9th

Last Answer : Solution :- Infinitely many equations.

Draw the graph of the following equations (1) Y =3x+2 (b) Y=x -Maths 9th

Description : Draw the graph of the following equations (1) Y =3x+2 (b) Y=x -Maths 9th

Last Answer : This answer was deleted by our moderators...

What is the angle between the lines whose equations are: 3x + y – 7 = 0 and x + 2y + 9 = 0. -Maths 9th

Description : What is the angle between the lines whose equations are: 3x + y – 7 = 0 and x + 2y + 9 = 0. -Maths 9th

Last Answer : (c) (8, 6)Let AB be the given line 4x + 3y = 25 Let O′(a, b) be the image of O in the given line AB. Let O O′ cut AB in point P. Also OP ⊥ AB and P is the mid-point of OO′. ∴ Co-ordinates of P are \(\bigg( ... 4 imes6}{3}\) = 8∴ The image of the point O(0, 0) in the line 4x + 3y - 25 = 0 is (8, 6).

Check whetherx =2 and y = 1 is a solution of the following equations or not. -Maths 9th

Description : Check whetherx =2 and y = 1 is a solution of the following equations or not. -Maths 9th

Last Answer : Given, x = 2 and y = 1 (i) Given, linear equation is 2x + 5y = 9. On putting x = 2 and y= 1 in LHS, we get LHS = 2x + 5y =2(2) + 5(1) = 4 + 5 = 9 = RHS So, x = 2 and y=1 is a solution of given ... + 3 (1) = 5 + 3 = 8 ≠ 14 ⇒ LHS ≠ RHS So, x = 2 and y = 1 is not a solution of given equation.

A student wrote the equations of the lines a and b drawn in the following graph as y =1 and 2x + 3y =6. Is he right? -Maths 9th

Description : A student wrote the equations of the lines a and b drawn in the following graph as y =1 and 2x + 3y =6. Is he right? -Maths 9th

Last Answer : Clearly, line a is parallel to X-axis at a distance of 1 unit in positive direction of Y-axis, therefore its equation is y = 1. Also, if we draw the graph of line 2x + 3y = 6, then its graph should intersect X - axis at (3,0 ... Base Height = 1/2 BC AC = 1/2 1 3 / 2 = 3 / 4 sq unit.

Check whetherx =2 and y = 1 is a solution of the following equations or not. -Maths 9th

Description : Check whetherx =2 and y = 1 is a solution of the following equations or not. -Maths 9th

Last Answer : Given, x = 2 and y = 1 (i) Given, linear equation is 2x + 5y = 9. On putting x = 2 and y= 1 in LHS, we get LHS = 2x + 5y =2(2) + 5(1) = 4 + 5 = 9 = RHS So, x = 2 and y=1 is a solution of given ... + 3 (1) = 5 + 3 = 8 ≠ 14 ⇒ LHS ≠ RHS So, x = 2 and y = 1 is not a solution of given equation.

A student wrote the equations of the lines a and b drawn in the following graph as y =1 and 2x + 3y =6. Is he right? -Maths 9th

Description : A student wrote the equations of the lines a and b drawn in the following graph as y =1 and 2x + 3y =6. Is he right? -Maths 9th

Last Answer : Clearly, line a is parallel to X-axis at a distance of 1 unit in positive direction of Y-axis, therefore its equation is y = 1. Also, if we draw the graph of line 2x + 3y = 6, then its graph should intersect X - axis at (3,0 ... Base Height = 1/2 BC AC = 1/2 1 3 / 2 = 3 / 4 sq unit.

What is distance between the graphs of the equations y = -1 and y = 3? -Maths 9th

Description : What is distance between the graphs of the equations y = -1 and y = 3? -Maths 9th

Last Answer : Solution :- 4 units.

Find the values of k for which the equations x^2 – kx – 21 = 0 and x^2 – 3kx + 35 = 0 will have a common root? -Maths 9th

Description : Find the values of k for which the equations x^2 – kx – 21 = 0 and x^2 – 3kx + 35 = 0 will have a common root? -Maths 9th

Last Answer : Let the common root be α ⟹α2−kα−21=0......(1) α2−3kα+35=0........(2) (1)−(2)⟹2kα=56⟹α=k28​Substituting α=k28​ in (1) (k28​)2−28−21=0 ⟹k=±4

If two equations x^2 + a^2 = 1 – 2ax and x^2 + b^2 = 1 – 2bx have only one common root, then -Maths 9th

Description : If two equations x^2 + a^2 = 1 – 2ax and x^2 + b^2 = 1 – 2bx have only one common root, then -Maths 9th

Last Answer : x2+b2=1−2bx ...... (i) x2+b2+2bx=1 (x+b)2=1 x+b= 1 ∴x=1−b,−1−b x2+a2=1−2ax ...... (ii) x2+a2+2ax=1 (x+a)2=1 ∴x=1−a,−1−a It is given that the equations have only one root in ... or −1−a=−b−1 we get a=b but then both roots will be common, which is not possible. Hence, options A,B and C are correct.

Use the graph to solve the system of linear equations x - y=4 4x + y=1?

Description : Use the graph to solve the system of linear equations x - y=4 4x + y=1?

Last Answer : x=4+y4x+y=1 = 4(4+y)+y=116+4y+y=116+5y=15y=-15y=-3x=4+y = x=4+(-3)x=1

In the following equations , verify whether the given value of the variable is a solution of the equation : -Maths 9th

Description : In the following equations , verify whether the given value of the variable is a solution of the equation : -Maths 9th

Last Answer : (i) If we substitute x = 4, we get L.H.S = x + 4 = 4 + 4 = 8 and R.H.S = 2x = 2 x 4 = 8 ∴ L.H.S = R.H.S. Hence, 4 is a solution of x + 4 = 2x. (ii) If we substitute y = 3, we get L.H.S = y - 7 = 3 - ... S = 2u + 7 = 2(5) + 7 = 10 + 7 = 17 ∴ L.H.S = R.H.S. Hence , 5 is a solution of 3u + 2 = 2u + 7

In the following equations , verify whether the given value of the variable is a solution of the equation : -Maths 9th

Description : In the following equations , verify whether the given value of the variable is a solution of the equation : -Maths 9th

Last Answer : (i) f we substitute x = √2, we get L.H.S. = 2x - 3 = 2(√2) - 3 = 2√2 - 3 and R.H.S = x / 2 - 2 = √2 / 2 - 2 ∴ L.H.S. ≠ R.H.S . Hence, √2 is not a solution of 2x - 3 = x / 2 - 2 (ii) If we substitute ... = 7 ∴ L.H.S. ≠ R.H.S . Hence , -1 is not a solution of 24 - 3 (u - 2) = u + 8

In the following equations , verify whether the given value of the variable is a solution of the equation : -Maths 9th

Description : In the following equations , verify whether the given value of the variable is a solution of the equation : -Maths 9th

Last Answer : (i) If we substitute x = 4, we get L.H.S = x + 4 = 4 + 4 = 8 and R.H.S = 2x = 2 x 4 = 8 ∴ L.H.S = R.H.S. Hence, 4 is a solution of x + 4 = 2x. (ii) If we substitute y = 3, we get L.H.S = y - 7 = 3 - ... S = 2u + 7 = 2(5) + 7 = 10 + 7 = 17 ∴ L.H.S = R.H.S. Hence , 5 is a solution of 3u + 2 = 2u + 7

In the following equations , verify whether the given value of the variable is a solution of the equation : -Maths 9th

Description : In the following equations , verify whether the given value of the variable is a solution of the equation : -Maths 9th

Last Answer : (i) f we substitute x = √2, we get L.H.S. = 2x - 3 = 2(√2) - 3 = 2√2 - 3 and R.H.S = x / 2 - 2 = √2 / 2 - 2 ∴ L.H.S. ≠ R.H.S . Hence, √2 is not a solution of 2x - 3 = x / 2 - 2 (ii) If we substitute ... = 7 ∴ L.H.S. ≠ R.H.S . Hence , -1 is not a solution of 24 - 3 (u - 2) = u + 8

Write three possible linear equations which can pass through point (3, –2). -Maths 9th

Description : Write three possible linear equations which can pass through point (3, –2). -Maths 9th

Last Answer : Solution :-

Give the equations of two lines passing through (4, –2). How many more such lines are there, and why? -Maths 9th

Description : Give the equations of two lines passing through (4, –2). How many more such lines are there, and why? -Maths 9th

Last Answer : Solution :-

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

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

Examine the nature of the roots of the equations: (i) 2x^2 + 2x + 3 = 0 -Maths 9th

Description : Examine the nature of the roots of the equations: (i) 2x^2 + 2x + 3 = 0 -Maths 9th

Last Answer : answer:

Of the following quadratic equations, which is the one whose roots are 2 and – 15 ? -Maths 9th

Description : Of the following quadratic equations, which is the one whose roots are 2 and – 15 ? -Maths 9th

Last Answer : answer:

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:

Solve for x: 5(4x + 3) = 3(x -2) -Maths 9th

Description : Solve for x: 5(4x + 3) = 3(x -2) -Maths 9th

Last Answer : Solution :-

Solve the equation 2x + 1 = x -3, and represent the solution(s) on (i) the number line. (ii) the Cartesian plane. -Maths 9th

Description : Solve the equation 2x + 1 = x -3, and represent the solution(s) on (i) the number line. (ii) the Cartesian plane. -Maths 9th

Last Answer : Solution :-

Solve for x: Sol. 3x/7 + 2/7 + 4(x + 1)/5 = 2/3(2x + 1) -Maths 9th

Description : Solve for x: Sol. 3x/7 + 2/7 + 4(x + 1)/5 = 2/3(2x + 1) -Maths 9th

Last Answer : Solution :-

Solve for x if a > 0 and 2 logx a + logax a + 3 loga2x a = 0 -Maths 9th

Description : Solve for x if a > 0 and 2 logx a + logax a + 3 loga2x a = 0 -Maths 9th

Last Answer : (d) \(a^{-rac{4}{3}}\)Since logaxa = \(rac{1}{log_aax}\) = \(rac{1}{log_aa+log_ax}\) = \(rac{1}{1+log_ax}\) andloga2x a = \(rac{1}{log_aa^2x}\) = \(rac{1}{log_aa^2+log_{ax}x}\) = \(rac{1}{2log_aa+log_{ax}x}\)= \( ... 2}}\)When t = \(-rac{4}{3}\), logax = \(-rac{4}{3}\) ⇒ \(x\) = \(a^{-rac{4}{3}}\)

Solve x^2 – 5x + 4 > 0. -Maths 9th

Description : Solve x^2 – 5x + 4 > 0. -Maths 9th

Last Answer : answer:

Solve (|x – 1| – 3) (|x + 2| – 5) < 0. Then -Maths 9th

Description : Solve (|x – 1| – 3) (|x + 2| – 5) < 0. Then -Maths 9th

Last Answer : Case 1. |x-1|-3>0 |x+2|–53, |x+2|

Solve : 4^(1 + x) + 4^(1 – x) = 10 for x. -Maths 9th

Description : Solve : 4^(1 + x) + 4^(1 – x) = 10 for x. -Maths 9th

Last Answer : answer:

Solve : (x + 1) (x + 2) (x + 3) (x + 4) + 1 = 0 -Maths 9th

Description : Solve : (x + 1) (x + 2) (x + 3) (x + 4) + 1 = 0 -Maths 9th

Last Answer : answer:

Two students A and B solve an equation of the form x^2 + px + q = 0. A starts with a wrong value of p and obtains the roots as 2 and 6. -Maths 9th

Description : Two students A and B solve an equation of the form x^2 + px + q = 0. A starts with a wrong value of p and obtains the roots as 2 and 6. -Maths 9th

Last Answer : Let αα and ββ be the roots of the quadratic equation x2+px+q=0x2+px+q=0 Given that, A starts with a wrong value of p and obtains the roots as 2 and 6. But this time q is correct. i.e., a product of roots ... 1 Now, from Eqs. (ii) and (iii), we get α=−3 and β=−4α=−3 and β=−4 which are correct roots.

Solve for x : log10 [log2 (log39)] = x -Maths 9th

Description : Solve for x : log10 [log2 (log39)] = x -Maths 9th

Last Answer : answer:

√3-1÷√3+1 rationalise (can solve by finding the rationalizing factor of denominator -Maths 9th

Description : √3-1÷√3+1 rationalise (can solve by finding the rationalizing factor of denominator -Maths 9th

Last Answer : This answer was deleted by our moderators...

√3-1÷√3+1 rationalise (can solve by finding the rationalizing factor of denominator -Maths 9th

Description : √3-1÷√3+1 rationalise (can solve by finding the rationalizing factor of denominator -Maths 9th

Last Answer : This answer was deleted by our moderators...

Using identities solve 103^ -Maths 9th

Description : Using identities solve 103^ -Maths 9th

Last Answer : NEED ANSWER

Using identities solve 103^ -Maths 9th

Description : Using identities solve 103^ -Maths 9th

Last Answer : FRIEND YOUR QUESTION IS NOT CLEAR

Solve the equation u-5 =15 and state the axiom that you use here. -Maths 9th

Description : Solve the equation u-5 =15 and state the axiom that you use here. -Maths 9th

Last Answer : Solution :-

A can solve 90% of the problems given in a book and B can solve 70%. What is the probability that at least one of them -Maths 9th

Description : A can solve 90% of the problems given in a book and B can solve 70%. What is the probability that at least one of them -Maths 9th

Last Answer : Let E be the event that A solve the problem and F the event that B solves the problem.Then P(E) = \(rac{90}{100}\) = \(rac{9}{10}\), P(F) =\(rac{70}{100}\) = \(rac{7}{10}\), P(\(\bar{E}\) ... probability that at least one of them will solve a problem = 1 - \(rac{3}{100}\) = \(rac{97}{100}\) = 0.97.

Solve the following linear inequations: -Maths 9th

Description : Solve the following linear inequations: -Maths 9th

Last Answer : answer:

Solve the following pairs of inequations and also graph the solution set -Maths 9th

Description : Solve the following pairs of inequations and also graph the solution set -Maths 9th

Last Answer : answer:

Solve log2x + 3 (6x^2 + 23x + 21) = 4 – log3x + 7 (4x^2 + 12x + 9). -Maths 9th

Description : Solve log2x + 3 (6x^2 + 23x + 21) = 4 – log3x + 7 (4x^2 + 12x + 9). -Maths 9th

Last Answer : answer:

Is there a general way to solve equations involving both a multiple of x and a power of x?

Description : Is there a general way to solve equations involving both a multiple of x and a power of x?

Last Answer : Do they know about logarithms yet?

Solve the following equations `(i) (log_(2)(9-2^(x)))/(3-x)=1` `(ii) x^((log_(10)x+7)/(4))=10^((log_(10)x+1)` `(iii) (log_(10)(100x))^(2)+(log_(10)(10

Description : Solve the following equations `(i) (log_(2)(9-2^(x)))/(3-x)=1` `(ii) x^((log_(10)x+7)/(4))=10^((log_(10)x+1)` `(iii) (log_(10)(100x))^(2)+(log_(10)(10

Last Answer : Solve the following equations `(i) (log_(2)(9-2^(x)))/(3-x)=1` `(ii) x^((log_(10)x+7)/(4))=10^((log_(10)x+1 ... 1)` `(v)5^(2x)=3^(2x)+2.5^(x)+2.3^(x)`