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

Aug 15, 2015

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

Explanation:

$\textcolor{b l u e}{x} + 2 y = 6$.........equation $1$

$\textcolor{b l u e}{x} - 3 y = - 4$....equation $2$

Solving through elimination .
Subtracting equation $2$ from $1$

$\cancel{\textcolor{b l u e}{x}} + 2 y = 6$
$\cancel{- \textcolor{b l u e}{x}} + 3 y = + 4$

$5 y = 10$
color(blue)(y=2

Finding $x$ by substituting $y$ in equation $1$
$x + 2 y = 6$
$x + 2 \cdot 2 = 6$
$x = 6 - 4$
color(blue)(x=2