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.

Question

y=x+3

−4x+4y=28

(2 points)

Math Short Answer Rubric (2 points)
Points Awarded Criteria
2
The answer is correct. The student made no errors while solving.

The answer shows that the student used problem-solving skills and reasoning.

All work is shown or explained.

1
The answer is partially correct. The student made errors while solving.

The answer shows little problem-solving skills or reasoning.

Some work is shown or explained.

0 The question is not answered.

Answer 1

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 our two equations in the form y = mx + b:

1) y = x + 3
2) y = x + 7

Now we can graph these two lines on a coordinate plane. The first line y=x+3 has a y-intercept of 3 and a slope of 1, which means it goes up by 1 unit for every 1 unit it moves to the right.

The second line y=x+7 has a y-intercept of 7 and a slope of 1, which means it is parallel to the first line but higher up on the y-axis.

When we graph both lines, we can see that they are parallel and never intersect. This tells us that there is no solution to this system of linear equations, as the lines are parallel and will never cross.

Therefore, the system of equations is inconsistent.