Question

solve using elimination.
10x - 2y = -6
-8x - 5y = 18
(\boxed{ }, \boxed{ })
submit

Explanation:

Step1: Eliminate \( y \) by multiplying equations

Multiply the first equation \( 10x - 2y = -6 \) by \( 5 \) and the second equation \( -8x - 5y = 18 \) by \( 2 \) to make the coefficients of \( y \) opposites.
First equation after multiplication: \( 5(10x - 2y) = 5(-6) \) gives \( 50x - 10y = -30 \)
Second equation after multiplication: \( 2(-8x - 5y) = 2(18) \) gives \( -16x - 10y = 36 \)

Step2: Subtract the two equations to eliminate \( y \)

Subtract the second new equation from the first new equation:
\( (50x - 10y) - (-16x - 10y) = -30 - 36 \)
Simplify: \( 50x - 10y + 16x + 10y = -66 \)
Combine like terms: \( 66x = -66 \)

Step3: Solve for \( x \)

Divide both sides by \( 66 \): \( x = \frac{-66}{66} = -1 \)

Step4: Substitute \( x = -1 \) into one of the original equations to find \( y \)

Use the first original equation \( 10x - 2y = -6 \). Substitute \( x = -1 \):
\( 10(-1) - 2y = -6 \)
Simplify: \( -10 - 2y = -6 \)
Add \( 10 \) to both sides: \( -2y = -6 + 10 = 4 \)
Divide by \( -2 \): \( y = \frac{4}{-2} = -2 \)

Answer:

\((-1, -2)\)