Question

solve the system of equations
2x + 8y = 8
2x - 4y = -16

(_,_)

Answer 1

To solve the system of equations:

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

We can use the elimination or substitution method. Here, I will use the elimination method.

**Step 1: Simplify both equations if possible.**

Both equations can be simplified by dividing by 2:

- From Equation 1:
\[
x + 4y = 4 \quad \text{(Equation 1 simplified)}
\]

- From Equation 2:
\[
x - 2y = -8 \quad \text{(Equation 2 simplified)}
\]

**Step 2: Eliminate \(x\) by manipulating the equations.**

We can subtract Equation 2 from Equation 1 to eliminate \(x\):

\[
(x + 4y) - (x - 2y) = 4 - (-8)
\]

This simplifies to:

\[
6y = 12
\]

**Step 3: Solve for \(y\):**

\[
y = \frac{12}{6} = 2
\]

**Step 4: Substitute \(y\) back into one of the original equations to find \(x\).**

Let's substitute \(y = 2\) into the simplified Equation 1:

\[
x + 4(2) = 4
\]
\[
x + 8 = 4
\]
\[
x = 4 - 8 = -4
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-4, 2)
\]

**Final Answer:**

\[
(-4, 2)
\]