Solve the system of equations.

Question

2x+8y=8

2x−4y=−16
(1 point)
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Remaining Attempts

Answer 1

To solve the system of equations:

1. \( 2x + 8y = 8 \) (Equation 1)
2. \( 2x - 4y = -16 \) (Equation 2)

Let's simplify each equation first.

From Equation 1: \[ 2x + 8y = 8 \] Dividing the entire equation by 2: \[ x + 4y = 4 \quad (1) \]

From Equation 2: \[ 2x - 4y = -16 \] Dividing the entire equation by 2: \[ x - 2y = -8 \quad (2) \]

Now we can solve these two simplified equations:

1. \( x + 4y = 4 \)
2. \( x - 2y = -8 \)

Next, we can substitute \( x \) from Equation (2) into Equation (1).

From Equation (2), we can express \( x \) as: \[ x = -8 + 2y
\]

Now substitute this into Equation (1): \[ (-8 + 2y) + 4y = 4 \]

Combine like terms: \[ -8 + 6y = 4 \] Add 8 to both sides: \[ 6y = 12 \] Divide by 6: \[ y = 2 \]

Now substitute \( y = 2 \) back into the expression for \( x \): \[ x = -8 + 2(2) \] \[ x = -8 + 4 \] \[ x = -4 \]

So the solution to the system of equations is: \[ (x, y) = (-4, 2) \]

Final answer: \[ \boxed{(-4, 2)} \]