`3x=5y+19`
`2x+y=-x+7`
What ordered pair `(x, y)` represents the solution to the system of equations above?

Answer

To solve the system of equations:

1. **Write the equations:**
- Equation 1: \(3x = 5y + 19\)
- Equation 2: \(2x + y = -x + 7\)

2. **Rearrange Equation 1:**
- Move \(5y\) to the left side and \(19\) to the right side:
\[ 3x - 5y = 19 \]

3. **Rearrange Equation 2:**
- Move \(-x\) to the left side:
\[ 2x + x + y = 7 \implies 3x + y = 7 \]

4. **Now we have the system of equations:**
- Equation 1: \(3x - 5y = 19\)
- Equation 2: \(3x + y = 7\)

5. **Subtract Equation 2 from Equation 1:**
\[ (3x - 5y) - (3x + y) = 19 - 7 \]
- This simplifies to:
\[ -5y - y = 12 \implies -6y = 12 \]

6. **Solve for \(y\):**
\[ y = \frac{12}{-6} = -2 \]

7. **Substitute \(y = -2\) back into one of the original equations to find \(x\):**
- Using Equation 2:
\[ 3x + (-2) = 7 \]
- This simplifies to:
\[ 3x - 2 = 7 \]
- Add \(2\) to both sides:
\[ 3x = 9 \]
- Divide by \(3\):
\[ x = 3 \]

8. **The ordered pair \((x, y)\) is:**
\[ (3, -2) \]