# How do you solve the system x + y = 4 and y = -x + 1 by graphing?

May 14, 2018

The two equations have the same slope, $m = - 1$, therefore they are perpendicular and there is no solution to this linear system. The two lines have no points in common.

#### Explanation:

Solve system of linear equations by graphing.

$\text{Equation 1} :$ $x + y = 4$ $\leftarrow$ standard form

$\text{Equation 2} :$ $y = - x + 1$ $\leftarrow$ slope-intercept form

Convert Equation 1 to slope-intercept form.

$y = - x + 4$

The two equations have the same slope, $m = - 1$, therefore they are perpendicular and there is no solution to this linear system. The two lines have no points in common.

graph{(x+y-1)(x+y-4)=0 [-10, 10, -5, 5]}