  ### Home > A2C > Chapter 5 > Lesson 5.1.3 > Problem5-37

5-37.

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

1. $y = 3x − 5$
$y = −2x − 15$

Use substitution to solve the system.

The solution to the system is $(−2, −11).$ Describe what that tells you about the system.

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.

1. $y − 7 = −2x$
$4x + 2y = 14$

Rearrange the first equation so it's in $y=$ form. Then use substitution to solve.

See part (a).

1. $y = 2(x + 3)^2 − 5$
$y = 14x + 17$

Use substitution to solve the system.

The solutions to the system are $(2, 45)$ and $(−1, 3)$.

If you didn't get the solution given above, check to be sure you squared $(x + 3)$ correctly then distributed the $2$.

If you need help with the description, refer to More Help in part (a).

1. $y = 3(x − 2)^2 + 3$
$y = 6x − 12$

Refer to part (c).

How many solutions did you get? What does that tell you about the graphs?