Question

chapter liner equation in two variable .
please anyone solve this problem by elimination method. ​

Answer 1

$\large\underline{\sf{Solution-}}$

Given pair of linear equations are

$\rm :\longmapsto\:125x + 110y = 152000 - - - (1)$

and

$\rm :\longmapsto\:110x + 125y = 153500 - - - (2)$

On adding equation (1) and (2), we get

$\rm :\longmapsto\:235x + 235y = 305500$

$\rm :\longmapsto\:235(x +y) = 305500$

$\rm :\longmapsto\:x +y= 1300 - - - (3)$

On Subtracting equation (2) from (1), we get

$\rm :\longmapsto\:15x - 15y = - 1500$

$\rm :\longmapsto\:15(x - y) = - 1500$

$\rm :\longmapsto\:x - y = - 100 - - - (4)$

Now, Adding equation (3) and (4), we get

$\rm :\longmapsto\:2x = 1200$

$\bf\implies \:x = 600 - - - (5)$

On substituting the value of x in equation (4), we get

$\rm :\longmapsto\:600 - y = - 100$

$\rm :\longmapsto\:- y = - 100 - 600$

$\rm :\longmapsto\:- y = - 700$

$\bf\implies \:y = 700$

Verification :-

Consider equation (1),

$\rm :\longmapsto\:125x + 110y = 152000$

On substituting the value of x and y, we get

$\rm :\longmapsto\:125(600) + 110(700) = 152000$

$\rm :\longmapsto\:75000 + 77000 = 152000$

$\rm :\longmapsto\:152000 = 152000$

Hence, Verified

Additional Information :-

Short - Cut trick to evaluate the linear equation of the form

$\rm :\longmapsto\:ax + by = c$

and

$\rm :\longmapsto\:bx + ay = d$

Then, such equations reduces to simplest form as

$\boxed{ \sf{x + y = \frac{c + d}{a + b}}}$

and

$\boxed{ \sf{x - y = \frac{c - d}{a - b}}}$