Question

Solve the system by Elimination

x−3y=7

3x+3y=9


(1 point)
Responses

(2,3)
(2,3)

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

(-3,2)
(-3,2)

(5,0)

Answer 1

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

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

**Step 1: Simplify Equation 2**
We can simplify Equation 2 by dividing everything by 3:

\[
x + y = 3 \quad (Equation 3)
\]

**Step 2: Set Up for Elimination**
Now, we can write the two equations we need to work with:

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

**Step 3: Multiply Equation 3 for Elimination**
To eliminate \(x\) by subtracting the two equations, we can multiply Equation 3 by -1:

\[
-x - y = -3 \quad (Equation 4)
\]

**Step 4: Add Equation 1 and Equation 4**
Now we will add Equation 1 and Equation 4 together:

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

This simplifies to:

\[
-4y = 4
\]

**Step 5: Solve for \(y\)**
Now, divide both sides by -4:

\[
y = -1
\]

**Step 6: Substitute \(y\) back into Equation 3 to find \(x\)**
We can substitute \(y = -1\) into Equation 3:

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

This simplifies to:

\[
x - 1 = 3
\]

Adding 1 to both sides gives:

\[
x = 4
\]

**Step 7: The solution**
So the solution to the system is:

\[
(x, y) = (4, -1)
\]

The correct answer is **(4, -1)**.