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)

Answer 1

shorter

Answer 2

To graph the first equation y = x + 3, we can start by plotting two points and then connecting them. Let's choose x = 0. Substituting x = 0 into y = x + 3, we get y = 0 + 3 = 3. So, one point on the line is (0, 3). Let's choose another value for x, say x = 2. Substituting x = 2 into y = x + 3, we get y = 2 + 3 = 5. So, another point on the line is (2, 5). We can now plot these two points and connect them with a straight line:

|
6 +
|
5 + . (2, 5)
|
4 +
|
3 + . (0, 3)
|
------------------
0 1 2 3 4 5 6

Now, we need to graph the second equation -4x + 4y = 28. To do this, we can solve for y:

-4x + 4y = 28
4y = 4x + 28
y = x + 7

We can use the same technique as before to find two points to plot. Let's choose x = 0. Substituting x = 0 into y = x + 7, we get y = 0 + 7 = 7. So, one point on the line is (0, 7). Let's choose another value for x, say x = 2. Substituting x = 2 into y = x + 7, we get y = 2 + 7 = 9. So, another point on the line is (2, 9). We can now plot these two points and connect them with a straight line:

|
10 +
|
9 +
|
8 +
|
7 + . (0, 7)
|
6 +
|
-------------------
0 1 2 3 4 5 6

Now, looking at the graph, we can see that the two lines intersect at the point (4, 7). This means that the solution to the system of linear equations is x = 4 and y = 7.