Solve for: {\text{begin}array l 4x-6y=4 } 5x-6y=2\text{end}array .

Expression: $\left\{\begin{array} { l } 4x-6y=4 \\ 5x-6y=2\end{array} \right.$

Move the variable to the right-hand side and change its sign

$\left\{\begin{array} { l } -6y=4-4x \\ 5x-6y=2\end{array} \right.$

Move the variable to the right-hand side and change its sign

$\left\{\begin{array} { l } -6y=4-4x \\ -6y=2-5x\end{array} \right.$

Since both expressions $4-4x$ and $2-5x$ are equal to $-6y$, set them equal to each other forming an equation in $x$

$4-4x=2-5x$

Solve the equation for $x$

$x=-2$

Substitute the given value of $x$ into the equation $-6y=2-5x$

$-6y=2-5 \times \left( -2 \right)$

Solve the equation for $y$

$y=-2$

The possible solution of the system is the ordered pair $\left( x, y\right)$

$\left( x, y\right)=\left( -2, -2\right)$

Check if the given ordered pair is the solution of the system of equations

$\left\{\begin{array} { l } 4 \times \left( -2 \right)-6 \times \left( -2 \right)=4 \\ 5 \times \left( -2 \right)-6 \times \left( -2 \right)=2\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 4=4 \\ 2=2\end{array} \right.$

Since all of the equalities are true, the ordered pair is the solution of the system

$\left( x, y\right)=\left( -2, -2\right)$