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Solve the following system of equations:
[tex]\[
\left\{
\begin{array}{l}
2x + 3y = 10 \\
x + y = 12
\end{array}
\right.
\][/tex]
Isolate [tex]\(x\)[/tex] by subtracting 36 from both sides: [tex]\[
-x = 10 - 36 \implies -x = -26
\][/tex]
Multiply both sides by -1: [tex]\[
x = 26
\][/tex]
4. Substitute the value of [tex]\(x\)[/tex] back into the expression for [tex]\(y\)[/tex]:
Recall from step 1 that [tex]\(y = 12 - x\)[/tex]: [tex]\[
y = 12 - 26
\][/tex]
Simplify: [tex]\[
y = -14
\][/tex]
5. Verify the solution:
Substitute [tex]\(x = 26\)[/tex] and [tex]\(y = -14\)[/tex] into both original equations to ensure that they are satisfied: [tex]\[
2x + 3y = 2(26) + 3(-14) = 52 - 42 = 10 \quad \text{(True)}
\][/tex]
[tex]\[
x + y = 26 + (-14) = 26 - 14 = 12 \quad \text{(True)}
\][/tex]
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