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Solve the system of equations: [tex]\[
\begin{cases}
12x + y = 14 \\
6x - 2 = 58
\end{cases}
\][/tex]
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]
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