CPM Homework Help : AC Problem 7-38

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7-38.

Find the point of intersection for each system of linear equations below. Be sure to check your solutions. Which method did you use for each system and why?

$\begin{aligned}[t] 5x - y &= 2 \\ 3x + y &= -10 \end{aligned}$
Hint (a):
Use the Elimination Method.
Step 1(a):
Add the equations together vertically.
The result is: $8x = −8$
Step 2(a):
Solve for $x$ by dividing the equation by $8$ . $x = −1$
Step 3(a):
Substitute $x$ into one of the original equations to find $y$ . $5\left(−1\right) − y = 2$
Step 4(a):
Solve for $y$ .
$y = −7$
Answer (a):
$\left(−1, −7\right)$

$\begin{aligned}[t] 6x &+ 2y = 7 \\ 4x &+ y = 4 \end{aligned}$
Hint (b):
Use the Elimination Method.
Step 1(b):
Multiply the 2nd equation by $−2$
Steps (b):
Follow the steps outlined in part (a).

$\begin{aligned}[t] 5x + 2y & = 7 \\ 2y + 5x & =7 \end{aligned}$
Hint (c):
Try rewriting the 2nd equation. What do you notice?

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