Question

Find the value of x and y :
$23x-29y=98$
$29x-23y=110$

Answer 1

Consider the given equation

$23x-29y=98.........\left(1\right)$

$29x-23y=110.........\left(2\right)$

Adding equation (1) and (2) to and we get,

$23x-29y=98$

$\underset{–}{29x-23y=110}$

$52x-52y=208$

$52(x-y)=208$

$x-y=4........\left(3\right)$

Subtracting equation (1) and (2) to and we get,

$23x-29y=98$

$\underset{–}{29x-23y=110}$

$-+-$

$-6x-6y=-12$

$-6(x+y)=-12$

$x+y=2.........\left(4\right)$

Solving equation (3) and (4) , and we get,

$x-y=4$

$\underset{–}{x+y=2}onadding$

$2x=6$

$x=3$

Put the value of x in equation (4) and we get,

$3+y=2$

$y=2-3=-1$

Hence, this is the solution.