Question

Solve the system of linear equations using substitution. 2x + y = -11 3x - 4y = 11 (1 point) Responses (5,3) (5,3) (-5,-3) (-5,-3) (3,5) (3,5) (-3,-5)

Answer 1

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

1. **Choose one equation to solve for one variable.** Let's solve the first equation for \(y\):

\[
2x + y = -11
\]

Rearranging gives:

\[
y = -11 - 2x \quad \text{(1)}
\]

2. **Substitute this expression for \(y\) into the second equation.** Using the second equation:

\[
3x - 4y = 11
\]

Substituting \(y\) from equation (1):

\[
3x - 4(-11 - 2x) = 11
\]

This simplifies to:

\[
3x + 44 + 8x = 11
\]

Combining like terms:

\[
11x + 44 = 11
\]

3. **Solve for \(x\):**

Subtract 44 from both sides:

\[
11x = 11 - 44
\]
\[
11x = -33
\]

Divide by 11:

\[
x = -3
\]

4. **Now substitute \(x = -3\) back into equation (1) to find \(y\):**

\[
y = -11 - 2(-3)
\]
\[
y = -11 + 6
\]
\[
y = -5
\]

5. **So, the solution to the system of equations is:**

\[
(x, y) = (-3, -5)
\]

From the given responses, the correct answer is:

\((-3, -5)\)