Type the correct answer in each box. If necessary, use / for the fraction bar(s).

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]



Answer :

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]