# How do you solve the linear equation x-y =12 and 2x+y=3 using the substitution method?

Jun 11, 2018

$\left(x , y\right) \to \left(5 , - 7\right)$

#### Explanation:

$x - y = 12 \to \left(1\right)$

$2 x + y = 3 \to \left(2\right)$

$\text{from equation } \left(2\right) \to y = 3 - 2 x \to \left(3\right)$

$\textcolor{b l u e}{\text{substitute "y=3-2x" into equation }} \left(1\right)$

$x - \left(3 - 2 x\right) = 12$

$x - 3 + 2 x = 12$

$\text{add 3 to both sides}$

$3 x = 15$

$\text{divide both sides by 3}$

$x = \frac{15}{3} = 5$

$\text{substitute "x=5" into equation } \left(3\right)$

$y = 3 - 10 = - 7$

$\text{point of intersection } = \left(5 , - 7\right)$
graph{(y+2x-3)(y-x+12)((x-5)^2+(y+7)^2-0.04)=0 [-20, 20, -10, 10]}