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 \((1, 2)\).