Question

se the graphing method to solve the system of linear equations:

y = -x + 3 and y = x - 1
Responses
A (-1,2)(-1,2)
B (0,3)(0,3)
C (1,0)(1,0)
D (1,2)(1,2)
E (2,1)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of linear equations using the graphing method, we need to plot the lines represented by the two equations on a graph and find the point of intersection.

For the first equation, y = -x + 3, we can start by assigning different values to x and solving for y to get a set of points. Let's assign x = 0, -1, and 1:

For x = 0, y = -0 + 3 = 3, so we have the point (0, 3).

For x = -1, y = -(-1) + 3 = 1 + 3 = 4, so we have the point (-1, 4).

For x = 1, y = -(1) + 3 = -1 + 3 = 2, so we have the point (1, 2).

Now let's plot these points and draw a line through them.

For the second equation, y = x - 1, we follow the same process:

For x = 0, y = 0 - 1 = -1, so we have the point (0, -1).

For x = -1, y = -1 - 1 = -2, so we have the point (-1, -2).

For x = 1, y = 1 - 1 = 0, so we have the point (1, 0).

Let's plot these points and draw a line through them.

Now we can see that the two lines intersect at the point (1, 2). Therefore, the correct option is:

D (1,2)(1,2)