Algebra and Trigonometry

# Review Exercises

Algebra and TrigonometryReview Exercises

### Review Exercises

##### Systems of Linear Equations: Two Variables

For the following exercises, determine whether the ordered pair is a solution to the system of equations.

1.

$3x−y=4 x+4y=−3 3x−y=4 x+4y=−3$ and $(−1,1) (−1,1)$

2.

$6x−2y=24 −3x+3y=18 6x−2y=24 −3x+3y=18$ and $(9,15) (9,15)$

For the following exercises, use substitution to solve the system of equations.

3.

$10x+5y=−5 3x−2y=−12 10x+5y=−5 3x−2y=−12$

4.

$4 7 x+ 1 5 y= 43 70 5 6 x− 1 3 y=− 2 3 4 7 x+ 1 5 y= 43 70 5 6 x− 1 3 y=− 2 3$

5.

$5x+6y=14 4x+8y=8 5x+6y=14 4x+8y=8$

For the following exercises, use addition to solve the system of equations.

6.

$3x+2y=−7 2x+4y=6 3x+2y=−7 2x+4y=6$

7.

$3x+4y=2 9x+12y=3 3x+4y=2 9x+12y=3$

8.

$8x+4y=2 6x−5y=0.7 8x+4y=2 6x−5y=0.7$

For the following exercises, write a system of equations to solve each problem. Solve the system of equations.

9.

A factory has a cost of production $C(x)=150x+15,000 C(x)=150x+15,000$ and a revenue function $R(x)=200x. R(x)=200x.$ What is the break-even point?

10.

##### Solving Systems with Cramer's Rule

For the following exercises, find the determinant.

71.

$| 100 0 0 0 | | 100 0 0 0 |$

72.

$| 0.2 −0.6 0.7 −1.1 | | 0.2 −0.6 0.7 −1.1 |$

73.

$| −1 4 3 0 2 3 0 0 −3 | | −1 4 3 0 2 3 0 0 −3 |$

74.

$| 2 0 0 0 2 0 0 0 2 | | 2 0 0 0 2 0 0 0 2 |$

For the following exercises, use Cramer’s Rule to solve the linear systems of equations.

75.

$4x−2y=23 −5x−10y=−35 4x−2y=23 −5x−10y=−35$

76.

$0.2x−0.1y=0 −0.3x+0.3y=2.5 0.2x−0.1y=0 −0.3x+0.3y=2.5$

77.

$−0.5x+0.1y=0.3 −0.25x+0.05y=0.15 −0.5x+0.1y=0.3 −0.25x+0.05y=0.15$

78.

$x+6y+3z=4 2x+y+2z=3 3x−2y+z=0 x+6y+3z=4 2x+y+2z=3 3x−2y+z=0$

79.

$4x−3y+5z=− 5 2 7x−9y−3z= 3 2 x−5y−5z= 5 2 4x−3y+5z=− 5 2 7x−9y−3z= 3 2 x−5y−5z= 5 2$

80.

$3 10 x− 1 5 y− 3 10 z=− 1 50 1 10 x− 1 10 y− 1 2 z=− 9 50 2 5 x− 1 2 y− 3 5 z=− 1 5 3 10 x− 1 5 y− 3 10 z=− 1 50 1 10 x− 1 10 y− 1 2 z=− 9 50 2 5 x− 1 2 y− 3 5 z=− 1 5$