Systems of Linear Equations Unit Test
14 of 1414 of 14 Items
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
(2 points)
To graph the system of equations y=x+3 and -4x+4y=28, we first need to rewrite the second equation in slope-intercept form.
Starting with the second equation -4x+4y=28, we can simplify it to y=x+7 by dividing by 4 on both sides.
Now we have the two equations y=x+3 and y=x+7.
When we graph these two equations, we see that they are parallel lines with the same slope but different y-intercepts. This means that the lines will never intersect, indicating that there is no solution to this system of linear equations.
This can also be confirmed algebraically by solving for x and y in both equations and seeing that there are no values that satisfy both equations simultaneously.