# How do you solve the following system of equations?: 2x + y = 8 , -2x +3y=12?

$x = \frac{3}{2} , \setminus \setminus y = 5$

#### Explanation:

The given equations

$2 x + y = 8 \setminus \ldots \ldots \ldots . . \left(1\right)$

$- 2 x + 3 y = 12 \setminus \ldots \ldots \ldots . . \left(2\right)$

Adding (1) & (2) as follows

$2 x + y + \left(- 2 x + 3 y\right) = 8 + 12$

$4 y = 20$

$y = \frac{20}{4} = 5$

setting $y = 5$ in (1), we get

$2 x + 5 = 8$

$2 x = 3$

$x = \frac{3}{2}$
The solution of given linear equations is $x = \frac{3}{2} , \setminus y = 5$