Question

Solve the system by Elimination

x - 3y = 7
3x + 3y = 9

(1 point)
Responses

(4,-1)
(4,-1)

(5,0)
(5,0)

(2,3)

Answer 1

To solve the system of equations using the elimination method, we start with the two given equations:

1) \( x - 3y = 7 \)
2) \( 3x + 3y = 9 \)

First, let's simplify the second equation. We can divide every term by 3:

\[
x + y = 3
\]

Now we have the simplified system:

1) \( x - 3y = 7 \)
2) \( x + y = 3 \)

Next, we'll use the elimination method. We'll eliminate \(x\) by aligning the equations. We can subtract the second equation from the first.

First, let's write the equations again:

1) \( x - 3y = 7 \)
2) \( x + y = 3 \)

We'll subtract the second equation from the first:

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

This simplifies to:

\[
-4y = 4
\]

Now, divide both sides by -4:

\[
y = -1
\]

Next, we substitute \(y = -1\) back into one of the original equations to find \(x\). We'll use the second equation \(x + y = 3\):

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

So,

\[
x - 1 = 3 \implies x = 4
\]

Now we have:

\[
x = 4 \quad y = -1
\]

Thus, the solution to the system of equations is:

\[
(4, -1)
\]

The correct response is:

**(4, -1)**