# How do you solve the following systems of equations by graphing given y=x-4, 2y=-x+10?

Jun 24, 2018

See a solution process below:

#### Explanation:

First, we need to graph each equation by solving each equation for two points and then drawing a straight line through the two points.

Equation 1:

First Point: For $x = 0$

$y = 0 - 4$

$y = - 4$ or $\left(0 , - 4\right)$

Second Point: For $x = 4$

$y = 4 - 4$

$y = 0$ or $\left(4 , 0\right)$

graph{(y - x + 4)(x^2+(y+4)^2-0.075)((x-4)^2+y^2-0.075)=0 [-10, 20, -6, 9]}

Equation 2:

First Point: For $x = 0$

$2 y = - 0 + 10$

$2 y = 10$

$\frac{2 y}{\textcolor{red}{2}} = \frac{10}{\textcolor{red}{2}}$

$y = 5$ or $\left(0 , 5\right)$

Second Point: For $x = 10$

$2 y = - 10 + 10$

$2 y = 0$

$\frac{2 y}{\textcolor{red}{2}} = \frac{0}{\textcolor{red}{2}}$

$y = 0$ or $\left(10 , 0\right)$

graph{(2y + x - 10)(y - x + 4)(x^2+(y-5)^2-0.075)((x-10)^2+y^2-0.075)=0 [-10, 20, -6, 9]}

From the graphs we can see the line intersects at: $\left(\textcolor{red}{6} , \textcolor{red}{2}\right)$

graph{(2y + x - 10)(y - x + 4)((x-6)^2+(y-2)^2-0.075) = 0 [-10, 20, -6, 9]}