Question

Solve for x and y:

$\frac{x}{2}-\frac{y}{9}=6,\frac{x}{7}+\frac{y}{3}=5.$

Answer 1

$\frac{x}{7}+\frac{y}{3}=5,\frac{x}{2}-\frac{y}{9}=6$

On taking LCM of denominators and simplifying, we get the linear equations as
3x + 7y = 105 → (1)

9x − 2y = 108 → (2)

Multiply equation(1) with 3 , we get

9x + 21y = 315 → (3)

Now subtract (2) from (3)

9x + 21y = 315
9x − 2y = 108
----------------------
23y = 207

∴ y =$\frac{207}{23}$ = 9

Put y = 9 in 3x + 7y = 105

3x + 7(9) = 105

⇒ 3x = 105 − 63 = 42

$\therefore x=\frac{42}{3}=14$