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 \( y = -1 \).