Question

solve the system of equation using the addition/elimination method.
x + 2y = 2
-4x + 3y = 25
(-1, 7)
(3, 25)
(-4, 3)
(0, 1)

Explanation:

Step1: Eliminate x by scaling first equation

Multiply \( x + 2y = 2 \) by 4: \( 4x + 8y = 8 \)

Step2: Add to second equation

Add \( 4x + 8y = 8 \) and \( -4x + 3y = 25 \):
\( (4x - 4x) + (8y + 3y) = 8 + 25 \)
\( 11y = 33 \)

Step3: Solve for y

Divide by 11: \( y = \frac{33}{11} = 3 \)

Step4: Substitute y into first equation

\( x + 2(3) = 2 \)
\( x + 6 = 2 \)
\( x = 2 - 6 = -4 \)

Answer:

\((-4, 3)\)