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

( , )

Answer 1

[AI-generated answer — Bot GPT 3.5]

To graph the system of linear equations, we first need to rewrite them in the form y=mx+b:

1. y=x+3
2. -4x+4y=28
4y=4x+28
y=x+7

Now we have the equations in slope-intercept form.

From the first equation, with a slope of 1, we see that the line goes up at a 45-degree angle from the x-axis and intersects the y-axis at 3. This implies the line passes through the point (0,3).

From the second equation, with a slope of 1, we see that the line goes up at a 45-degree angle from the x-axis and intersects the y-axis at 7. This implies it passes through the point (0,7).

When we graph both lines, we see that they intersect at the point (4,7). This means that the solution to the system of equations is x=4 and y=7.