How do you solve -4x+9y=9 and x-3y= -6?

Mar 15, 2018

See below.

Explanation:

$4 x + 9 y = 9 \text{ " " } \left(1\right)$

$x - 3 y = - 6 \text{ " " } \left(2\right)$

From equation $\left(2\right)$

$x - 3 y = - 6$

$\implies x = - 6 + 3 y \text{ " " } \left(3\right)$

Substituting in equation $\left(1\right)$

$\implies 4 \left(3 y - 6\right) + 9 y = 9$

$\implies 12 y - 24 + 9 y = 9$

$\implies 21 y = 9 + 24$

$\implies 21 = 33$

$\implies y = \frac{33}{21}$

$\implies y = \frac{11}{7}$

Substituting the value of $y$ in equation $\left(2\right)$

$x = 3 y - 6$

$\implies x = 3 \left(\frac{11}{7}\right) - 6$

$\implies x = \frac{33}{7} - 6$

$\implies x = \frac{33 - 42}{7}$

$\implies x = - \frac{9}{7}$

So

$x = - \frac{9}{7} \mathmr{and} y = \frac{11}{7}$