# How do you solve the following system?:  x + 2y = 6 , 2x - 3y = 5

Apr 4, 2018

$x = 4 \mathmr{and} y = 1$

#### Explanation:

$x + 2 y = 6 \text{ " " } \left(1\right)$
$2 x + 3 y = 5 \text{ " " } \left(2\right)$

Multiply equation $\left(1\right)$ by $3$ and equation $\left(2\right)$ by $2$,

3 xx (x +2y=6) 2 xx (2x -3y=5)#

Therefore,

$3 x + 6 y = 18 \text{ " " } \left(3\right)$
$4 x - 6 y = 10 \text{ " " } \left(4\right)$

Add equation $\left(3\right)$ to equation $\left(4\right)$

$7 x + 0 = 28$

Make $x$ the subject of the equation

$x = \frac{28}{7}$

$x = 4$

Substitute the value of $x$ in equation $\left(1\right)$

$x + 2 y = 6$

$4 + 2 y = 6$

Collect like terms

$2 y = 6 - 4$

$2 y = 2$

Divide through by $2$ to make $y$ the subject of the equation

$y = 1$

Ans:

$x = 4 \mathmr{and} y = 1$