Question

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

Answer 1

Solve the second equation for y: -4x + 4y = 28 ⇒ divide by 4 ⇒ -x + y = 7 ⇒ y = x + 7.

So the two lines are
- y = x + 3
- y = x + 7

Both have slope 1, but different y-intercepts (3 and 7). On a graph they are two parallel lines:

- y = x + 3 passes through (0,3), (1,4), (−1,2).
- y = x + 7 passes through (0,7), (1,8), (−1,6).

Because the lines are parallel, they never intersect. Therefore the system has no solution (it is inconsistent).