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 tells you about the solution on the system of linear equations.
y = x + 3
-4x + 4y = 28
To graph the system of linear equations, we can first rewrite the second equation in slope-intercept form:
-4x + 4y = 28
4y = 4x + 28
y = x + 7
Now we have the two equations:
y = x + 3
y = x + 7
When we graph these lines on a coordinate plane, we see that they are parallel lines with different y-intercepts. This means that there is no point of intersection between the two lines, therefore there is no solution to the system of linear equations.
In conclusion, the graph of the system of linear equations consists of two parallel lines that do not intersect, indicating that there is no solution.