Question

Find the solution of the system of equations.
5, x, plus, 8, y, equals, 5
5x+8y=
5
5, x, plus, 7, y, equals, 0
5x+7y=
0

Answer 1

To solve the system of equations:

1. \( 5x + 8y = 5 \) (Equation 1)
2. \( 5x + 7y = 0 \) (Equation 2)

We'll use the elimination method:

### Step 1: Subtract Equation 2 from Equation 1

\[
(5x + 8y) - (5x + 7y) = 5 - 0
\]

This simplifies to:

\[
8y - 7y = 5
\]

\[
y = 5
\]

### Step 2: Substitute \(y\) back into one of the original equations

Let's use Equation 2 (\(5x + 7y = 0\)):

\[
5x + 7(5) = 0
\]

\[
5x + 35 = 0
\]

\[
5x = -35
\]

\[
x = -7
\]

### Step 3: Write the solution

The solution to the system of equations is:

\[
(x, y) = (-7, 5)
\]