Question

Solve the system below using substitution. Show step-by-step work to earn credit. Use the Formula Editor x−−√ to type math or use the Image icon to upload a photo of your work.

y=−x+5
3x+y=11

Answer 1

To solve the system of equations using substitution, we’ll follow these steps:

1. **Identify the equations**:
\[
\text{Equation 1: } y = -x + 5
\]
\[
\text{Equation 2: } 3x + y = 11
\]

2. **Substitute Equation 1 into Equation 2**: Since we have \(y\) expressed in terms of \(x\) in Equation 1, we can substitute \(-x + 5\) for \(y\) in Equation 2.

So, substituting into Equation 2:
\[
3x + (-x + 5) = 11
\]

3. **Simplify the equation**:
Combine like terms:
\[
3x - x + 5 = 11
\]
\[
2x + 5 = 11
\]

4. **Solve for \(x\)**:
Subtract 5 from both sides:
\[
2x = 11 - 5
\]
\[
2x = 6
\]

Now divide by 2:
\[
x = \frac{6}{2}
\]
\[
x = 3
\]

5. **Substitute back to find \(y\)**:
Now that we have \(x\), substitute \(3\) back into Equation 1 to find \(y\):
\[
y = -x + 5
\]
\[
y = -3 + 5
\]
\[
y = 2
\]

6. **Solution**: The solution to the system of equations is:
\[
(x, y) = (3, 2)
\]

So, the final answer is:
\[
\boxed{(3, 2)}
\]

Let’s verify the solution by plugging \(x = 3\) and \(y = 2\) back into both original equations.

- Checking Equation 1:
\[
y = -x + 5
\]
\[
2 = -3 + 5 \quad \text{(True)}
\]

- Checking Equation 2:
\[
3x + y = 11
\]
\[
3(3) + 2 = 9 + 2 = 11 \quad \text{(True)}
\]

The solution \((3, 2)\) satisfies both equations. Thus, it is correct.