Question

−3x−10=y
−x−8y=11

Answer 1

To solve the system of equations given by:

1. \( -3x - 10 = y \)
2. \( -x - 8y = 11 \)

we can use substitution or elimination. Here, we'll use substitution.

### Step 1: Substitute \( y \) from the first equation into the second equation.

From the first equation, we can express \( y \) in terms of \( x \):

\[
y = -3x - 10
\]

Now, we'll substitute this expression for \( y \) into the second equation:

\[
-x - 8(-3x - 10) = 11
\]

### Step 2: Solve for \( x \).

Expanding the second equation gives:

\[
-x + 24x + 80 = 11
\]

Combine like terms:

\[
23x + 80 = 11
\]

Now, isolate \( x \):

\[
23x = 11 - 80
\]
\[
23x = -69
\]
\[
x = -3
\]

### Step 3: Substitute \( x \) back to find \( y \).

Now, substitute \( x = -3 \) back into the expression for \( y \):

\[
y = -3(-3) - 10
\]

Calculate \( y \):

\[
y = 9 - 10
\]
\[
y = -1
\]

### Solution

The solution to the system of equations is:

\[
x = -3, \quad y = -1
\]

Thus, the solution in ordered pair form is:

\[
(-3, -1)
\]