CPM Homework Help : CC3MN Problem 10-112

CPM Homework Banner

Home > CC3MN > Chapter 10 > Lesson 10.4.1 > Problem 10-112

10-112.

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

$\begin{aligned}[t] -2x + 3y = 1 \\ 2x + 6y = 2 \;\; \end{aligned}$
Hint 1(a):
Use the Elimination Method.
Step (a):
$−2x+3y=1$
$2x+6y=2$
$9y=3$
Hint 2(a):
Find $y$ then input the answer into one of the equations above to find $x$ .
Answer (a):
$x=0\text{ and }y=\frac{1}{3}$

$\begin{aligned}[t] y = \frac{1}{3}x + 4 \\ x = - 3y \quad \; \end{aligned}$
Hint (b):
Use the Substitution Method. The equivalent of $x$ is already given.
Step (b):
$y=\frac{1}{3}(-3y)+4$
Answer (b):
$x=−6$ and $y=2$

$\begin{aligned}[t] 3x - y = 7 \\ y = 3x - 2 \end{aligned}$
Hint (c):
Refer to parts (a) and (b) for help. Be aware of the $−y$ in the first equation.

$\begin{aligned}[t] x + 2y = 1 \; \, \\ 3x + 5y = 8 \end{aligned}$
Hint (d):
Use the elimination method like in part (a).
More Help (d):
Multiply the first equation by $−3$ .

© 2022 CPM Educational Program. All rights reserved.