Certainly! Let's solve the given system of equations step-by-step:
The system of equations is:
[tex]\[
\begin{cases}
12x + y = 14 \quad &\text{(1)} \\
6x - 2 = 58 \quad &\text{(2)}
\end{cases}
\][/tex]
First, we need to simplify equation (2):
[tex]\[
6x - 2 = 58
\][/tex]
Add 2 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
6x = 58 + 2
\][/tex]
[tex]\[
6x = 60
\][/tex]
Now, divide both sides by 6 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{60}{6}
\][/tex]
[tex]\[
x = 10
\][/tex]
Next, we substitute [tex]\(x = 10\)[/tex] into equation (1) to find [tex]\(y\)[/tex]:
[tex]\[
12x + y = 14
\][/tex]
Substitute [tex]\(x = 10\)[/tex] into the equation:
[tex]\[
12(10) + y = 14
\][/tex]
[tex]\[
120 + y = 14
\][/tex]
Subtract 120 from both sides to solve for [tex]\(y\)[/tex]:
[tex]\[
y = 14 - 120
\][/tex]
[tex]\[
y = -106
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
x = 10 \quad \text{and} \quad y = -106
\][/tex]
Thus, the solution is [tex]\((10, -106)\)[/tex].
