Question

Consider this linear system:

3x − 2y = −2
x + 3y = 14
Which ordered pair is the solution to the system?
Responses
A (2, 4)(2, 4)
B (2, −4)(2, −4)
C (−2, 4)(−2, 4)
D (−2, −4)(−2, −4)

Answer 1

To solve the system of equations given by:

1. \( 3x - 2y = -2 \)
2. \( x + 3y = 14 \)

we can evaluate each of the answer choices by substituting the values of \( x \) and \( y \) into both equations.

**Option A: (2, 4)**

Substituting \( x = 2 \) and \( y = 4 \) into the first equation:
\[
3(2) - 2(4) = 6 - 8 = -2 \quad \text{(True)}
\]
Now substitute into the second equation:
\[
2 + 3(4) = 2 + 12 = 14 \quad \text{(True)}
\]
So, (2, 4) is a solution.

**Option B: (2, -4)**

Substituting \( x = 2 \) and \( y = -4 \) into the first equation:
\[
3(2) - 2(-4) = 6 + 8 = 14 \quad \text{(False)}
\]
Since it fails the first equation, (2, -4) is not a solution.

**Option C: (-2, 4)**

Substituting \( x = -2 \) and \( y = 4 \) into the first equation:
\[
3(-2) - 2(4) = -6 - 8 = -14 \quad \text{(False)}
\]
Since it fails the first equation, (-2, 4) is not a solution.

**Option D: (-2, -4)**

Substituting \( x = -2 \) and \( y = -4 \) into the first equation:
\[
3(-2) - 2(-4) = -6 + 8 = 2 \quad \text{(False)}
\]
Since it fails the first equation, (-2, -4) is not a solution.

The only viable solution is:

**A. (2, 4)**