CPM Homework Help : INT1 Problem 6-95

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6-95.

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

$\begin{aligned} [t] 2x + 3y = 9 \quad \; \, \\ -3x + 3y = -6 \end{aligned}$

Step 1(a):
One strategy to solve this system of equations is to multiply the bottom equation by $-1$ so you can eliminate.
$2x+3y=9$
$3x-3y=6$
$5x=15$
Step 2(a):
After finding $x$ , plug in its value into one of the equations to find the value of $y$ .
Answer (a):
$x=3$
$y=1$

$\begin{aligned}[t] x = 8 - 2y \\ y - x = 4 \; \; \end{aligned}$

Hint (b):
Because one of the equations above is already solved for $x$ , one strategy to solve this system is to substitute the first equation in for $x$ in the second equation.

$\begin{aligned}[t] y = -\frac{1}{2}x + 7 \\ y = x - 8 \quad \; \; \, \end{aligned}$

Hint (c):
Use the Equal Values Method.

$\begin{aligned}[t] 9x + 10y = 14 \\ 7x + 5y = -3 \, \end{aligned}$

Hint (d):
Refer to part (a).
Answer (d):
$x=-4;y=5$

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