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Solving a System of Equations

Examine the system of equations:

[tex]\[
\begin{array}{c}
5x + 6y = 32 \\
5x - 6y = 8
\end{array}
\][/tex]

1. Which variable or variables will be eliminated when you add the system of equations?
[tex]\[\square\][/tex]

2. Which equation results from adding the system of equations?
[tex]\[\square\][/tex]

Sagot :

GinnyAnsweridn
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].
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