Question

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

Answer 1

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.

`"Equation 1":` `x+y=4` `larr` standard form

`"Equation 2":` `y=-x+1` `larr` 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]}