Question

4x +8y=20
-4x+2y=-30
elimination standard

Answer 1

To solve the system of equations using the elimination method, we have the following equations:

1. \( 4x + 8y = 20 \) (Equation 1)
2. \(-4x + 2y = -30\) (Equation 2)

The goal is to eliminate one variable by adding or subtracting the equations. Let's first line them up for clarity:

\[
\begin{align*}
1) & \quad 4x + 8y = 20 \\
2) & \quad -4x + 2y = -30
\end{align*}
\]

**Step 1: Add the equations to eliminate \(x\)**

Adding Equation 1 and Equation 2 together:

\[
(4x + 8y) + (-4x + 2y) = 20 + (-30)
\]

This simplifies to:

\[
0 + 10y = -10
\]

**Step 2: Solve for \(y\)**

\[
10y = -10
\]
\[
y = -1
\]

**Step 3: Substitute \(y\) back into one of the original equations to find \(x\)**

We'll use Equation 1:

\[
4x + 8(-1) = 20
\]
\[
4x - 8 = 20
\]
\[
4x = 28
\]
\[
x = 7
\]

**Final Solution:**

The solution to the system of equations is:

\[
(x, y) = (7, -1)
\]

**Verification:**

We can check by substituting \(x = 7\) and \(y = -1\) into both original equations:

For Equation 1:
\[
4(7) + 8(-1) = 28 - 8 = 20 \quad \text{(True)}
\]

For Equation 2:
\[
-4(7) + 2(-1) = -28 - 2 = -30 \quad \text{(True)}
\]

Both equations check out, confirming that the solution is correct: \( (x, y) = (7, -1) \).