Question

9×x-11×y=49 ,13×x-12×y=63 so find the value of x and y

Answer 1

It is a lengthy questions because of calculations.

Answer 2

Given:

Two linear equations in two variables:

9x - 11y = 49 .... (1)

and 13x - 12y = 63 .... (2)

To Find:

The values of x & y.

Solution:

We will solve the question using elimination method.

Lets eliminate the terms with 'x', for that we'll have to make the x- coefficients same.

We will multiply equation (1) with 13 and equation (2) with 9, and then we will subtract equation (2) from (1).

13 $\times$ {9x - 11y = 49}

and, 9 $\times$ {13x - 12y = 63}

We get,

117x - 143y = 637

and, 117x - 108y = 567

Lets subtact these equations, (which means subtracting the LHS from LHS and RHS from RHS of another equation).

117x - 143y - (117x - 108y) = 637 -567

which gives, 117x - 143y - 117x + 108y = 70

implies, -143y +108y = 70

$\Rightarrow$ -35y = 70

$\Rightarrow y = \frac{70}{-35}$

$\Rightarrow$ y = -2

Now, lets put this value in equation (1) and solve for x:

9x - 11(-2) = 49

$\Rightarrow$ 9x +22 = 49

$\Rightarrow$ 9x = 49 -22

$\Rightarrow$ 9x = 27

$\Rightarrow x = \frac{27}{9}$

$\Rightarrow$ x = 3

Therefore, the values of x & y are 3 and -2 respectively.