Question

solve using elimination.
6x + 2y = 2
-4x + y = 15
(□, □)
submit

Explanation:

Step1: Multiply the second equation by 2

To eliminate \( y \), we multiply the second equation \(-4x + y = 15\) by 2. This gives us \(-8x + 2y = 30\).

Step2: Subtract the new second equation from the first equation

The first equation is \( 6x + 2y = 2 \) and the new second equation is \(-8x + 2y = 30\). Subtracting the second from the first: \((6x + 2y) - (-8x + 2y) = 2 - 30\). Simplifying the left side: \(6x + 2y + 8x - 2y = 14x\), and the right side: \(-28\). So \(14x = -28\).

Step3: Solve for \( x \)

Divide both sides of \(14x = -28\) by 14: \(x = \frac{-28}{14} = -2\).

Step4: Substitute \( x = -2 \) into the second original equation to find \( y \)

Substitute \( x = -2 \) into \(-4x + y = 15\): \(-4(-2) + y = 15\). Simplify: \(8 + y = 15\). Subtract 8 from both sides: \(y = 15 - 8 = 7\).

Answer:

\((-2, 7)\)