Answered

In order to solve this system using the substitution method, what would be the first step?

[tex]\[
\left\{\begin{array}{l}
x + 2y = 10 \\
7x - 5y = 12
\end{array}\right.
\][/tex]

A. Set the equations equal to each other.
B. Add the equations together.
C. Solve one of the equations for one variable.
D. Draw the graph of the equations.



Answer :

GinnyAnswer
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.

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