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Find the solution for this system of equations. [tex]\[
\begin{array}{l}
2x - 3y = 2 \\
x = 6y - 5 \\
x = \square \\
y = \square
\end{array}
\][/tex]
To find the solution for the system of equations, follow these steps:
1. Write down the system of equations: [tex]\[
\begin{aligned}
2x - 3y &= 2 \\
x &= 6y - 5
\end{aligned}
\][/tex]
2. Substitute \( x \) from the second equation into the first equation: [tex]\[
2(6y - 5) - 3y = 2
\][/tex]
3. Simplify and solve for \( y \): [tex]\[
12y - 10 - 3y = 2
\][/tex] [tex]\[
9y - 10 = 2
\][/tex] [tex]\[
9y = 12
\][/tex] [tex]\[
y = \frac{12}{9} = \frac{4}{3}
\][/tex]
4. Substitute \( y = \frac{4}{3} \) back into the second equation to solve for \( x \): [tex]\[
x = 6 \left(\frac{4}{3}\right) - 5
\][/tex] [tex]\[
x = 8 - 5
\][/tex] [tex]\[
x = 3
\][/tex]
Therefore, the solutions to the system of equations are: [tex]\[
x = 3 \\
y = \frac{4}{3}
\][/tex]
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