Solve the system using elimination.

To solve the system of equations using elimination, we start with the two equations you've provided:

1. \( 3x + 2y = 88 \) (Equation 1)
2. \( 7x - 2y = 1212 \) (Equation 2)

We can eliminate one of the variables by adding the two equations together. To do this effectively, we can add the two equations since the coefficients of \( y \) will cancel each other out.

Step 1: Add the equations together

Add Equation 1 and Equation 2:

\[ (3x + 2y) + (7x - 2y) = 88 + 1212 \]

Step 2: Simplify

The \( 2y \) and \( -2y \) will cancel out:

\[ 3x + 7x = 88 + 1212 \]

Combining like terms gives us:

\[ 10x = 1300 \]

Step 3: Solve for \( x \)

Now, divide both sides by 10:

\[ x = \frac{1300}{10} = 130 \]

Step 4: Substitute \( x \) back to find \( y \)

Now that we have \( x = 130 \), we can substitute this value back into either of the original equations to find \( y \). We'll use Equation 1:

\[ 3x + 2y = 88 \]

Substituting \( x = 130 \):

\[ 3(130) + 2y = 88 \]

Calculating \( 3(130) \):

\[ 390 + 2y = 88 \]

Step 5: Solve for \( y \)

Now, isolate \( 2y \):

\[ 2y = 88 - 390 \] \[ 2y = -302 \]

Dividing both sides by 2:

\[ y = \frac{-302}{2} = -151 \]

Step 6: Write the solution

Thus, the solution to the system of equations is:

\[ x = 130, \quad y = -151 \]

Final Answer:

\( (130, -151) \)