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]
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]
