Question

our 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 ordered pair that is a solution to the system of equations given by \(y = 3x + 2\) and \(y = -2x + 12\), we can start by calculating the values of \(y\) for the provided \(x\) values in each equation.

Let's take the given values: \(x = -2, -1, 0, 1, 2\).

### For the equation \(y = 3x + 2\):
1. When \(x = -2\):
\(y = 3(-2) + 2 = -6 + 2 = -4\)

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

3. When \(x = 0\):
\(y = 3(0) + 2 = 0 + 2 = 2\)

4. When \(x = 1\):
\(y = 3(1) + 2 = 3 + 2 = 5\)

5. When \(x = 2\):
\(y = 3(2) + 2 = 6 + 2 = 8\)

### For the equation \(y = -2x + 12\):
1. When \(x = -2\):
\(y = -2(-2) + 12 = 4 + 12 = 16\)

2. When \(x = -1\):
\(y = -2(-1) + 12 = 2 + 12 = 14\)

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

4. When \(x = 1\):
\(y = -2(1) + 12 = -2 + 12 = 10\)

5. When \(x = 2\):
\(y = -2(2) + 12 = -4 + 12 = 8\)

### Summary of results:

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

### Identify the intersection:

Looking at the results, we can see that for \(x = 2\), both equations yield \(y = 8\). Therefore, the ordered pair \((2, 8)\) is a solution to the system of equations.

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