# How do you solve this system of equations: 7x - 2y = 12; 4x + 5y = 13?

Mar 5, 2018

$\textcolor{b l u e}{x = 2 , y = 1}$

#### Explanation:

$7 x - 2 y = 12$ Eqn (1)

$7 x - 12 = 2 y$

$y = \frac{7 x}{2} - 6$

$4 x + 5 y = 13$ Eqn (2)

Substituting value of y in terms of x in Eqn (2),

$4 x + 5 \left(\left(7 \frac{x}{2}\right) - 6\right) = 13$

$4 x + \frac{35 x}{2} = 13 + 30 = 43$

$43 x = 2 \cdot 43 = 86$

$x = 2$

Substituting value of x in Eqn (2),

$y = \frac{7 \cdot 2}{2} - 6 = 1$