Question

Find the solution to the system of equations given below using elimination by addition.

10x + 10y = 60
5x - 5y = 40
A.
x = -7, y = 9

B.
x = 7, y = 1

C.
x = 10, y = 2

D.
x = 7, y = -1

Answer 1

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

1. \( 10x + 10y = 60 \)
2. \( 5x - 5y = 40 \)

First, we can simplify both equations.

### Simplifying the equations:
1. Divide the first equation by 10:
\[
x + y = 6 \quad \text{(Equation 1)}
\]

2. Divide the second equation by 5:
\[
x - y = 8 \quad \text{(Equation 2)}
\]

### Now we can use elimination:
We will add Equation 1 and Equation 2 together.

\[
\begin{align*}
(x + y) + (x - y) &= 6 + 8 \\
x + y + x - y &= 14 \\
2x &= 14 \\
x &= 7
\end{align*}
\]

### Now substitute \(x = 7\) back into one of the simplified equations to find \(y\):
Using Equation 1:
\[
7 + y = 6 \\
y = 6 - 7 \\
y = -1
\]

### The solution is:
\[
x = 7, \quad y = -1
\]

### Therefore, the solution to the system of equations is:
\[
\text{D. } (x = 7, y = -1)
\]