PreCalculus Unit 7 Review

7.1

100

Solve by Substitution.    3x+2y=16     x=2y

(4, 2)

200

Solve by Elimination

 x-3y=6

-3x+y=6

( -3,-3)

300

Solve by graphing

x² +3x=y

y=x²

(0,0)

400

Determine whether the ordered triple (3,-2,1) is a solution to the system. 

x+y+z=2

6x-4y+5z=31

5x+2y+2z=13

Yes, the triple (3,-2,1) is a solution. 

500

Solve by Elimination

2x+3y=2

4x+6y=4

Infinitely many solutions

7.2

100

[-2  2  1] + [1  3 -1]

[-1  5  0]

200

Find the additive inverse of the Matrix

[2  -1   2 ]

[4   3   0 ]

[-2   1  -2]

[-4  -3   0]

300

-4 [ 4  0]

    [1  -1]

[-16  0]

[-4    4]

400

[1 2 3]  times   [1    2]

[4 1 0]             [0   -1]

[2 0 1].            [1    4]

Solution

[4       12]

[4        7]

[3        8]

500

Find the multiplicative inverse of the following matrix

[4   3]

[2   2]

[ 1     -3/2 ]

[-1          2] 

7.3

100

Solve (Use Triangular Form)   

x -2y + z =2

-2x +2y -2z=3

-x +2y +z=-2 

(-5, -3.5, 0)

200

Solve by row-echelon and reduced-row echelon

x+2y−z=4

2x+y+z=−2

x+2y+z=2

(-10/6 , 7/3, -1)

300

Solve using inverse Matrices

x-3y+3z=-4

2x+37-z=15

4x-3y-z=19

(5, 1, -2)

400

Find Reduced Row Echelon. Solve.

5r +2s=0

     -3t=12

6s+5t=10

(-2,5,-4)

500

Solve

2x   -y  + z =10

4x +2y -3z =10

x.   -3y +2z=8

(4, 0, 2)

7.5

100

What are the boundaries of 

y>2x+3 and y < 3x

y=2x + 3

y=3x

200

Solve by Graphing

Y=< 2x +1

y> x²

Graph

300

Solve the system of inequality

y= 2x+5

y=2x

No solution

400

Solve the System 

x² + y²<9

y=3

No solution

500

Solve by graphing or algebraically

y²<=-x²+25

y=5

(0,5)

Bonus

400

Find x-y

2x-4y=5

x+2y=2

x-y=2.25-(-.124)=2.375