Question

Solving by using elimination (algebra 1)
4x + 8y = 20
-4x + 2y = -30

Answer 1

To solve the system of equations using the elimination method, we start with the two equations:

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

The goal of the elimination method is to eliminate one of the variables by adding or subtracting the equations.

Let's add Equation 1 and Equation 2:

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

Simplifying both sides:

\[
4x - 4x + 8y + 2y = 20 - 30
\]
\[
0 + 10y = -10
\]

Now, we can solve for \(y\):

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

Next, we'll substitute \(y = -1\) back into one of the original equations to find the value of \(x\). We'll use Equation 1:

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

Now we have the solution:

\[
x = 7, \quad y = -1
\]

Thus, the solution to the system of equations is \( (x, y) = (7, -1) \).