Solve 3x2 - 5y3 = -2 x2 + y2 = 136 x=11754 y=9457

Solve $\frac{3 x}{2}$ - $\frac{5 y}{3}$ = -2; $\frac{x}{2}$ + $\frac{y}{2}$ = $\frac{13}{6}$

$x = \frac{117}{54}, y = \frac{94}{57}$

$x = \frac{94}{57}, y = \frac{51}{19}$

$x = \frac{51}{19}, y = \frac{94}{57}$

$y = \frac{117}{54}, x = \frac{94}{57}$

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$\frac{3 x}{2}$ - $\frac{5 y}{3}$ = -2

Multiply by 6 on both sides

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

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

Multiply by 6 on both sides

3x + 3y = 13 --------------(2)

(1) ⇒ $x = \frac{10 y - 12}{9}$ ............(3)

Substituting equation (3) in equation (2)

3[ $\frac{10 y - 12}{9}$ ] + 3y = 13

10y - 12 + 9y = 39

19y = 51

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

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