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]
