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
Skip to navigation

Answer 1

To find the solution to the system of equations, we need to determine where the two lines intersect. We can do this by setting the two equations equal to each other, or by evaluating both equations at the given x-values.

The equations are:
1. \( y = 3x + 2 \)
2. \( y = -2x + 12 \)

Let's create a table for the given x-values and calculate the corresponding y-values.

Let's compute for each x-value:

- For \( x = -2 \):
- \( y = 3(-2) + 2 = -6 + 2 = -4 \)
- \( y = -2(-2) + 12 = 4 + 12 = 16 \)

- For \( x = -1 \):
- \( y = 3(-1) + 2 = -3 + 2 = -1 \)
- \( y = -2(-1) + 12 = 2 + 12 = 14 \)

- For \( x = 0 \):
- \( y = 3(0) + 2 = 0 + 2 = 2 \)
- \( y = -2(0) + 12 = 0 + 12 = 12 \)

- For \( x = 1 \):
- \( y = 3(1) + 2 = 3 + 2 = 5 \)
- \( y = -2(1) + 12 = -2 + 12 = 10 \)

- For \( x = 2 \):
- \( y = 3(2) + 2 = 6 + 2 = 8 \)
- \( y = -2(2) + 12 = -4 + 12 = 8 \)

Now let's summarize this information in a table:

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

From the table, we can see that when \( x = 2 \), both equations give the same \( y \)-value of 8.

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