Solve the following system of linear equations by graphing. 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

Question

−4x+4y=28

Answer 1

To solve this system of linear equations by graphing, we first need to rewrite the second equation in slope-intercept form.

Starting with the second equation:
−4x + 4y = 28
We can simplify by dividing by 4:
y = x + 7

Now we have the two equations:
y = x + 3
y = x + 7

Both equations have a slope of 1, meaning the lines will be parallel and never intersect. This indicates that there is no solution to this system of linear equations because the lines are parallel and will never cross on the graph.

Upon graphing these two lines, you would see two parallel lines with the same slope but different y-intercepts. This visualization confirms that the system has no solution.