### Home > CCA > Chapter Ch4 > Lesson 4.2.5 > Problem4-81

4-81.

Solve the following systems of equations using any method. Check each solution, if possible.

1. \begin{aligned}[t]-2x+3y=1\\2x+6y=2\end{aligned}

Use the Elimination Method.

$−2x+3y=1$
$2x+6y=2$
$9y=3$

Find $y$ then input the answer into one of the equations above to find $x$.

$x=0\text{ and }y=\frac{1}{3}$

1. \begin{aligned}[t]y&={\textstyle\frac{1}{3}}x+4\\x&=-3y\end{aligned}

Use the Substitution Method. The equivalent of $x$ is already given.

$y=\frac{1}{3}(-3y)+4$

$x=−6$ and $y=2$

1. \begin{aligned}[t]3x-y=7\\y=3x−2\end{aligned}

Refer to parts (a) and (b) for help. Be aware of the $−y$ in the first equation.

1. \begin{aligned}[t]x+2y=1\\ 3x+5y=8\end{aligned}

Use the elimination method like in part (a).

Multiply the first equation by $−3$.