Question

What is the solution to the system of equations y = 3x +2
and y =−2x+12
?

Complete the table to support your answer.





(1 point)
x values y = 3x +2
y =−2x+12
-2
-1
0
1
2
The ordered pair that is a solution to the system of equations is
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Answer 1

To find the solution to the system of equations:

1. \( y = 3x + 2 \)
2. \( y = -2x + 12 \)

We can solve the system by substituting values of \( x \) into both equations and finding the corresponding \( y \) values.

Let's complete the table for \( x = -2, -1, 0, 1, 2 \):

### Table:

| \( x \) | \( y = 3x + 2 \) | \( y = -2x + 12 \) |
|-----------|-------------------|---------------------|
| **-2** | \( y = 3(-2) + 2 = -6 + 2 = -4 \) | \( y = -2(-2) + 12 = 4 + 12 = 16 \) |
| **-1** | \( y = 3(-1) + 2 = -3 + 2 = -1 \) | \( y = -2(-1) + 12 = 2 + 12 = 14 \) |
| **0** | \( y = 3(0) + 2 = 0 + 2 = 2 \) | \( y = -2(0) + 12 = 0 + 12 = 12 \) |
| **1** | \( y = 3(1) + 2 = 3 + 2 = 5 \) | \( y = -2(1) + 12 = -2 + 12 = 10 \) |
| **2** | \( y = 3(2) + 2 = 6 + 2 = 8 \) | \( y = -2(2) + 12 = -4 + 12 = 8 \) |

### Results:
Now we can summarize the \( y \) values obtained for both equations:

- For \( x = -2 \): \( y = -4 \) and \( y = 16 \)
- For \( x = -1 \): \( y = -1 \) and \( y = 14 \)
- For \( x = 0 \): \( y = 2 \) and \( y = 12 \)
- For \( x = 1 \): \( y = 5 \) and \( y = 10 \)
- For \( x = 2 \): \( y = 8 \) and \( y = 8 \)

### Intersection Point:
From the table, we see that the equations yield the same value for \( y \) when \( x = 2 \):

- For \( x = 2 \): \( y = 8 \) (from both equations)

Thus, the ordered pair that is a solution to the system of equations is \((2, 8)\).

### Final Answer:
The ordered pair that is a solution to the system of equations is \((2, 8)\).