Question

A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
5x - 9 =93
-6 - 9y =27

Answer 1

To eliminate a variable and solve the given system of equations, we can start by solving one of the equations for a variable.

Let's rewrite the system clearly:

1. \( 5x - 9 = 93 \)
2. \( -6 - 9y = 27 \)

**Step 1: Solve the first equation for \( x \)**

To isolate \( x \) in the first equation:

1. Add 9 to both sides:
\[
5x - 9 + 9 = 93 + 9
\]
\[
5x = 102
\]

2. Now divide both sides by 5:
\[
x = \frac{102}{5}
\]
\[
x = 20.4
\]

Now that \( x \) is expressed in terms of a number, you can substitute it into the second equation to possibly eliminate it and solve for \( y \), or proceed to solve the second equation directly.

Alternatively, you could also solve the second equation for \( y \) first, but since the instructions specify to choose the correct first step, solving the first equation for \( x \) is a suitable choice.

So, the correct first step is to solve the first equation for \( x \).