Question

solve using elimination.
3x - 2y = 5
-3x + y = 2
(\boxed{ }, \boxed{ })

Explanation:

Step1: Add the two equations

To eliminate \( x \), we add the equations \( 3x - 2y = 5 \) and \( -3x + y = 2 \).

$$
LATEXBLOCK0
$$

Step2: Solve for \( y \)

Multiply both sides by -1 to solve for \( y \):
\( y = -7 \)

Step3: Substitute \( y \) into one equation

Substitute \( y = -7 \) into the second equation \( -3x + y = 2 \):

$$
LATEXBLOCK1
$$

Step4: Solve for \( x \)

Add 7 to both sides:
\( -3x = 2 + 7 = 9 \)
Divide both sides by -3:
\( x = \frac{9}{-3} = -3 \)

Answer:

\((-3, -7)\)