−3x−10=y

−x−8y=11

1 answer

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:

\[ (-3, -1) \]