# How do you solve the system of equations: 2x + 3y = 6, x + y = 4?

Aug 8, 2015

The solution for the system of equations is
color(blue)(x=6, y=-2

#### Explanation:

$\textcolor{b l u e}{2 x} + 3 y = 6$......equation $\left(1\right)$

$x + y = 4$, multiplying this equation by $2$
$\textcolor{b l u e}{2 x} + 2 y = 8$.....equation $\left(2\right)$

Solving by elimination , subtracting equation $2$ from $1$ results in elimination of color(blue)(2x

$\cancel{\textcolor{b l u e}{2 x}} + 3 y = 6$
$- \cancel{\textcolor{b l u e}{2 x}} - 2 y = - 8$

color(blue)(y=-2

Substituting the value of $y$ in equation $2$ to find $x$
$x + y = 4$

$x = 4 - y$

$x = 4 - \left(- 2\right)$

color(blue)(x=6