To find the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] for the given equation [tex]\(y = -3x - 4\)[/tex] using the provided table values, we can follow these steps:
### Step 1: Utilizing the values from the table
The table given is:
[tex]\[
\begin{tabular}{l|l|l|l}
$x$ & 89 & \mid 48 & \\
\hline
$y$ & & -164 & \\
\end{tabular}
\][/tex]
We need to find the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] given the equation [tex]\(y = -3x - 4\)[/tex].
### Step 2: Solving for [tex]\(x\)[/tex] when [tex]\(y\)[/tex] is given
From the table, it is known that [tex]\(y = -164\)[/tex] for an unknown value of [tex]\(x\)[/tex].
So, we start by solving the equation for [tex]\(x\)[/tex]:
[tex]\[
y = -3x - 4
\][/tex]
[tex]\[
-164 = -3x - 4
\][/tex]
First, isolate the term involving [tex]\(x\)[/tex]:
[tex]\[
-164 + 4 = -3x
\][/tex]
[tex]\[
-160 = -3x
\][/tex]
Now, solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-160}{-3}
\][/tex]
[tex]\[
x \approx 53.33
\][/tex]
### Step 3: Solving for [tex]\(y\)[/tex] when [tex]\(x\)[/tex] is given
Next, we'll plug the value [tex]\(x = 89\)[/tex] from the table to find [tex]\(y\)[/tex]:
[tex]\[
y = -3x - 4
\][/tex]
[tex]\[
y = -3(89) - 4
\][/tex]
[tex]\[
y = -267 - 4
\][/tex]
[tex]\[
y = -271
\][/tex]
So, the detailed, step-by-step solutions yield:
- When [tex]\(y = -164\)[/tex], [tex]\(x \approx 53.33\)[/tex]
- When [tex]\(x = 89\)[/tex], [tex]\(y = -271\)[/tex]
