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

Apr 18, 2016

color(blue)(x=3
color(blue)(y =9

Explanation:

$y = 2 x + 3$.............equation $\left(1\right)$

color(blue)(y = - x +12.........equation $\left(2\right)$

Solving by substitution.
Substituting equation $2$ in $1$:

$y = 2 x + 3$

$\textcolor{b l u e}{- x + 12} = 2 x + 3$

$12 - 3 = 2 x + x$

$9 = 3 x$

$x = \frac{9}{3}$

color(blue)(x=3

Finding $y$ from equation $1$:
$y = 2 x + 3$

$y = 2 \cdot \textcolor{b l u e}{\left(3\right)} + 3$

$y = 6 + 3$

color(blue)(y =9