Question

Solve the system using elimination.
left brace Start 2 By 1 Matrix 1st Row 1st Column nothing 2nd Row 1st Column nothing EndMatrix

x
plus
3 y
equals
3
5 x
plus
5 y
equals
negative 5
Question content area bottom
Part 1
Select the correct choice below and fill in any answer boxes in your choice.
A.
The solution is
  
enter your response here. ​(Type an ordered​ pair.)
B.
There are infinitely many solutions.
C.
There is no solution.

Answer 1

To solve the system of equations using elimination, we have the following equations:

1. \( x + 3y = 3 \) (Equation 1)
2. \( 5x + 5y = -5 \) (Equation 2)

Let's rearrange Equation 2 to make it easier to work with:

\[ 5x + 5y = -5 \]

We can simplify this equation by dividing every term by 5:

\[ x + y = -1 \] (Equation 3)

Now, we have a new system of equations:

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

Next, we can eliminate \(x\) by subtracting Equation 3 from Equation 1:

\[
(x + 3y) - (x + y) = 3 - (-1)
\]

This simplifies to:

\[
3y - y = 3 + 1
\]

\[
2y = 4
\]

Now, solving for \(y\):

\[
y = 2
\]

Next, we substitute the value of \(y\) back into Equation 3 to find \(x\):

\[
x + y = -1
\]
\[
x + 2 = -1
\]

Solving for \(x\):

\[
x = -1 - 2
\]
\[
x = -3
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-3, 2)
\]

### Final Answer:

A. The solution is \((-3, 2)\).