Question

A variable needs to be eliminated to solve the system of equations. Choose the correct first step.
-9x - 7=24
9x - y =-48

Answer 1

To eliminate a variable from the system of equations, it's often useful to align them so that one of the variables can be canceled out when combined. Let's take a look at both equations first:

1. \(-9x - 7 = 24\)
2. \(9x - y = -48\)

First, we simplify the first equation to isolate \(y\):
\[
-9x - 7 = 24 \quad \Rightarrow \quad -9x = 24 + 7 \quad \Rightarrow \quad -9x = 31 \quad \Rightarrow \quad x = -\frac{31}{9}
\]

However, we can see that it's easier to eliminate \(y\) in the second equation by isolating it:
\[
y = 9x + 48
\]

With this isolated form of \(y\), we can substitute into the first equation. So, your first step could be solving the second equation for \(y\):
\[
y = 9x + 48
\]

Now you have \(y\) expressed in terms of \(x\), which allows for substitution into the first equation. Thus:

**The correct first step is to isolate \(y\) in the second equation: \(y = 9x + 48\).**