Answer
Wage of a laborer: $\$152$
Wage of a concrete finisher: $\$ 160$
Work Step by Step
Let's note:
$x \rightarrow$ the wage of each laborer
$y \rightarrow$ the wage of each concrete finisher
Here, we have the a set of equations on the basis of given statements as follows:
$$ 7x+2y=1384 ~~(1) \\ x+5y =952 ~~~(2)$$
The matrix form for equations (1) and (2) would be as follows:
\[
\left[
\begin{array}{cc|c}
7 & 2 & 1384 \\
1 & 5 & 952
\end{array}
\right]
\]
Next, $R1 \rightarrow -7R2+R1$, we get:
\[
\left[
\begin{array}{cc|c}
0 & -33 & -5280 \\
1 & 5 & 952
\end{array}
\right]
\]
Now, divide $R1$ by $-33$
\[
\left[
\begin{array}{cc|c}
0 & 1 & 160 \\
1 & 5 & 952
\end{array}
\right]
\]
Next step would be multiply $R1$ by $-5$ and add it to $R2$
\[
\left[
\begin{array}{cc|c}
0 & 1 & 160 \\
1 & 0 & 152
\end{array}
\right]
\]
Hence, the required answers are: $x= \$152$ and $y =\$ 160$.
Thus, wage of laborers; $x= \$152$ and wage of concrete finishers $y =\$ 160$.
