To solve the given system of equations, follow these steps:
1. Write down the given system of equations:
[tex]\[
\begin{array}{c}
5x + 6y = 32 \\
5x - 6y = 8
\end{array}
\][/tex]
2. Add the two equations together:
[tex]\[
(5x + 6y) + (5x - 6y) = 32 + 8
\][/tex]
3. Combine the like terms:
[tex]\[
5x + 5x + 6y - 6y = 32 + 8
\][/tex]
[tex]\[
10x + 0y = 40
\][/tex]
4. Simplify the equation:
[tex]\[
10x = 40
\][/tex]
From these steps, we can determine the following:
- Which variable or variables will be eliminated when you add the system of equations?
- The variable [tex]\(y\)[/tex] will be eliminated.
- Which equation results from adding the system of equations?
- The resulting equation is [tex]\(10x = 40\)[/tex].
In summary, when we add the two given equations, the variable [tex]\(y\)[/tex] is eliminated, and the resulting equation is [tex]\(10x = 40\)[/tex].
