Question

Solve the linear system using the elimination method.3x+2y=7−3x+4y=5(1 point)Responses(5,5)open paren 5 comma 5 close paren(0,0)open paren 0 comma 0 close paren(3,−1)open paren 3 comma negative 1 close paren(1,2)

Answer 1

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

1. \(3x + 2y = 7\) (Equation 1)
2. \(-3x + 4y = 5\) (Equation 2)

### Step 1: Add the equations
We can eliminate \(x\) by adding both equations together:

\[
(3x + 2y) + (-3x + 4y) = 7 + 5
\]

This simplifies to:

\[
0x + 6y = 12
\]

or

\[
6y = 12
\]

### Step 2: Solve for \(y\)
Dividing both sides by 6 gives:

\[
y = 2
\]

### Step 3: Substitute \(y\) back to find \(x\)
Now we can substitute \(y = 2\) back into one of the original equations. Let's use Equation 1:

\[
3x + 2(2) = 7
\]

This simplifies to:

\[
3x + 4 = 7
\]

Subtracting 4 from both sides gives:

\[
3x = 3
\]

Dividing by 3:

\[
x = 1
\]

### Final solution
The solution to the system is \((x, y) = (1, 2)\).

Thus, the correct response is \((1, 2)\).