Solve and find value of y3x2−5y3=−2   x2+y2=136 y=11754

SOLUTION

$\frac{3x}{2}$ -  $\frac{5y}{3}$ = -2

LCM of 2 and 3  is 6. Multiply by 6 on both sides

$9x-10y=-12$ -------------(1)

$\frac{x}{2}+\frac{y}{2}=\frac{13}{6}$

LCM is 6. Multiply by 6 on both sides

$3x+3y=13$  --------------(2)

Multiply equation (2) by 3 to eliminate x ; so we get,

$9x+9y=39$...............(3)

 Subtract (3) from (1) we have

$-19y=-51\Rightarrow y=\frac{51}{19}$

Substitute this in one of the equation and we get

$x=10\left[\frac{\frac{51}{19}-12}{9}\right]=\frac{282}{19\times 9}=\frac{94}{3\times 19}=\frac{94}{57}$

$\Rightarrow x=\frac{94}{57}$