Linear system by the elimination method

Text

Solve the following system using the elimination method: $\begin{cases} 3y-2=x\\ 2x+6=3y \end{cases}$

Solution

Put the equations in standard form: $\begin{cases} x-3y=-2\\ 2x-3y=-6 \end{cases}$ Subtract the first from the second to eliminate $y$: $(2x-3y)-(x-3y)=-6-(-2)$, i.e. $x=-4$. Substituting into the first: $-4-3y=-2 \implies -3y=2 \implies y=-\dfrac23$. $\boxed{x=-4,\quad y=-\frac23}$