Solve the following system of linear equations by graphing. Graph on your own piece of paper. In your submitted answer, describe what the graph looks like and what this tells you about the solution to the system of linear equations. y=x+3 −4x+4y=28 (2 points)
To solve the system of linear equations by graphing, first rewrite the equations in slope-intercept form:
1) y = x + 3
2) -4x + 4y = 28
4y = 4x + 28
y = x + 7
Now we can graph the two lines y = x + 3 and y = x + 7 on the same coordinate plane.
The line y = x + 3 has a y-intercept at (0,3) and a slope of 1 (rise of 1, run of 1).
The line y = x + 7 has a y-intercept at (0,7) and a slope of 1 as well.
When we graph both lines, we see that the two lines are parallel and will never intersect. This tells us that there is no solution to the system of linear equations, as the lines are parallel and will never cross.