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. Please make it intended for 8th grade.
y=x+3
−4x+4y=28
To graph the system of linear equations, we will first put both equations in slope-intercept form which is y=mx+b.
1. y=x+3
The y-intercept is 3, and the slope is 1 (rise 1, run 1).
2. -4x+4y=28
Divide by 4 to get y by itself: y = x + 7
Now we have both equations in slope-intercept form:
1. y = x + 3
2. y = x + 7
When we graph these two lines on the same coordinate plane, we will see that they are parallel lines. This tells us that there is no solution to the system of equations because the lines will never intersect. The lines will have the same slope but different y-intercepts, hence they are parallel.
This means that the system of equations is inconsistent (no solution) because the lines do not cross.