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
To solve this system of linear equations by graphing, we first need to rewrite the second equation in slope-intercept form (y = mx + b):
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Now we have the following equations to graph:
y = x + 3
y = x + 7
When we graph these two equations, we see that they are parallel lines with the same slope of 1 but different y-intercepts. This means that the lines will never intersect and there is no solution to the system of linear equations.
The graph tells us that the system of equations is inconsistent and the lines do not intersect, which means there is no solution that satisfies both equations simultaneously.