# How do you solve the system of equations: x + 2y = 7, 2x + y = 8?

Aug 14, 2015

The solutions are
color(blue)(x=3,y=2

#### Explanation:

$x + 2 y = 7$, multiplying this equation by $2$
$\textcolor{b l u e}{2 x} + 4 y = 14$,.......equation $1$

$\textcolor{b l u e}{2 x} + y = 8$....equation $2$

Solving by elimination .

Subtracting equation $2$ from $1$ to eliminate color(blue)(2x

$\cancel{\textcolor{b l u e}{2 x}} + 4 y = 14$
$- \cancel{\textcolor{b l u e}{2 x}} - y = - 8$

$3 y = 6$
color(blue)(y=2

Now, we find $x$ by substituting $y$ in equation $1$
$x + 2 y = 7$

$x = 7 - 2 y$

$x = 7 - 2 \cdot 2$
$x = 7 - 4$
color(blue)(x=3