### Home > GB8I > Chapter 6 Unit 7 > Lesson INT1: 6.4.1 > Problem6-116

6-116.

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 = \frac{1}{3}x + 4 \\ x = - 3y \quad \; \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 $−3$.