Answer :
Answer:
To solve the system of equations using elimination, we'll aim to eliminate one of the variables by adding or subtracting the equations. Let's start by eliminating the variable \( x \).
Given:
\[
\begin{cases}
3x + 10y = -4 \\
2x + 2y = 2
\end{cases}
\]
We can eliminate \( x \) by multiplying the second equation by \( \frac{3}{2} \) to match the coefficient of \( x \) in the first equation:
\[
\begin{cases}
3x + 10y = -4 \\
3x + 3y = 3
\end{cases}
\]
Now, we can subtract the second equation from the first:
\[
\begin{cases}
(3x + 10y) - (3x + 3y) = (-4) - (3) \\
3x + 10y - 3x - 3y = -4 - 3 \\
7y = -7
\end{cases}
\]
Now, we can solve for \( y \):
\[
\begin{cases}
7y = -7 \\
y = -1
\end{cases}
\]
Now that we have \( y = -1 \), we can substitute this value into one of the original equations to solve for \( x \). Let's use the second equation:
\[
2x + 2(-1) = 2 \\
2x - 2 = 2 \\
2x = 2 + 2 \\
2x = 4 \\
x = 2
\]
So, the solution to the system of equations is \( x = 2 \) and \( y = -1 \).
