Question

question 13 of 25
use the elimination method to solve the system of equations. choose the correct ordered pair.
$-x + y = -3$
$3x + 2y = 9$
a. (6, 3)
b. (3, 0)
c. (4, 1)
d. (5, 2)

Explanation:

Step1: Multiply first equation by 2

To eliminate \( y \), multiply the equation \(-x + y = -3\) by 2. We get \( -2x + 2y = -6 \).

Step2: Subtract new equation from second equation

Subtract \(-2x + 2y = -6\) from \( 3x + 2y = 9 \). So, \((3x + 2y) - (-2x + 2y) = 9 - (-6)\). Simplifying, \( 3x + 2y + 2x - 2y = 15 \), which gives \( 5x = 15 \).

Step3: Solve for \( x \)

Divide both sides by 5: \( x = \frac{15}{5} = 3 \).

Step4: Substitute \( x = 3 \) into first equation

Substitute \( x = 3 \) into \(-x + y = -3\). We have \(-3 + y = -3\).

Step5: Solve for \( y \)

Add 3 to both sides: \( y = -3 + 3 = 0 \).

Answer:

B. (3, 0)