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3-49.

Solve each of the following systems algebraically. What do the solutions tell you about the graph of each system? Visualizing the graphs may help with your description.

$y=3x−5$
$y=−2x−15$
Hint (a):
Use substitution to solve the system.
Answer (a):
The solution to the system is $(−2,−11)$ .
Describe what that tells you about the system.
More Help (a):
If you can't visualize the system, graph both equations and look at the point $(−2,−11)$ .
If it doesn't look important, check your graphs.

$y−7=−2x$
$4x+2y=14$
Hint (b):
Rewrite the first equation so it's in $y$ = form. Then use substitution to solve.
More Help (b):
See part (a).

$y=2(x+3)^2−5$
$y=14x+17$
Hint (c):
Use substitution to solve the system.
Answer (c):
The solutions to the system are $(2,45)$ and $(−1,3)$ .
Help (c):
If you didn't get the solution given above, check to be sure you squared $(x+3)$ correctly then distributed the $2$ .
More Help (c):
If you need help with the description, refer to More Help in part (a).

$y=3(x−2)^2+3$
$y=6x−12$
Hint (d):
Refer to part (c).
More Help (d):
How many solutions did you get? What does that tell you about the graphs?

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