To solve the system of equations using the substitution method, the first step involves manipulating the equations to isolate one variable. Starting with the given system of equations:
[tex]\[
\begin{cases}
x + 2y = 10 \\
7x - 5y = 12
\end{cases}
\][/tex]
The first step is to solve one of these equations for one variable.
Let’s solve the first equation for [tex]\(x\)[/tex]:
1. Begin with the first equation:
[tex]\[
x + 2y = 10
\][/tex]
2. Rearrange the equation to isolate [tex]\(x\)[/tex]:
[tex]\[
x = 10 - 2y
\][/tex]
Now you have expressed [tex]\(x\)[/tex] in terms of [tex]\(y\)[/tex]. This is the required first step in the substitution method.
So, the correct answer is:
Solve one of the equations for one variable.
