Ch. 3 Test Rework
Intermediate Algebra
Name __________________Per ___
You can turn this in as many times as needed before Christmas break. Each problem needs to be
100% correct before receiving credit. That means you need to have 100% correct work with the
correct answer. You can receive up to a maximum of 50% of the points you lost on your test. To
receive credit, I must have your original test or it will not be accepted. You do not need to do
problems you already got correct on your test. You are welcome to work on the extra credit
problem as well.
Solve the system using the substitution method. (6 pts)
Problem 1.
1) 3x + 7y = 22
x – 2y = -10
2) 2x + 5y = 23
x – 3y = -16
3) 4x + 7y = 30
x – 9y = -57
Solve the system using the elimination method. (6 pts)
Problem 2.
1) 4x – 6y = -62
4x + y = -6
2) 2x – 5y = -18
4x + y = -3
3) 3x – 6y = -19.5
8x + y = -35
Solve the system using Cramer’s Rule. (6 pts)
|𝑎𝑛𝑠𝑤𝑒𝑟 𝑐𝑜𝑙𝑢𝑚𝑛 𝑦 𝑐𝑜𝑙𝑢𝑚𝑛|
𝑥=
Problem 3.
|𝑥 𝑐𝑜𝑙𝑢𝑚𝑛 𝑦 𝑐𝑜𝑙𝑢𝑚𝑛|
1) 3x + y = -18
2x - 4y = 2
2) 2x + y = -11
3x - 5y = 16
3) 4x + y = -22
1x - 6y = 32
1
𝑦=
|𝑥 𝑐𝑜𝑙𝑢𝑚𝑛 𝑎𝑛𝑠𝑤𝑒𝑟 𝑐𝑜𝑙𝑢𝑚𝑛|
|𝑥 𝑐𝑜𝑙𝑢𝑚𝑛 𝑦 𝑐𝑜𝑙𝑢𝑚𝑛|
Solve the system using any algebraic method. (6 pts)
Problem 4.
1) 3x + y = 6
6x + 2y = 12
2) 4x + y = 6
8x + 2y = 12
3) 5x + y = 9
10x + 2y = 30
Tell whether the given ordered triple is a solution (Yes or No?). Make sure to show work. (6 pts)
Problem 5.
1) (3, -2, -1)
4x – y + 3z = 11
x + 2y + z = -2
x + 3y – 2z = -1
2) (5, -3, -4)
6x – y + 4z = 17
x + 5y + z = -14
x + 8y – 9z = 17
3) (8, -1, -2)
3x – y + 2z = 21
x + 6y + z = 0
x + 7y – 2z = -3
Solve the system using any algebraic method. (6: 6 pts)
Problem 6.
1) -2x + 8y = 2
7x + 4y = 41
2) -3x + 11y = -1.5
6x + 4y = 42
3) -4x + 8y = 8
7x + 2y = 26
2
Solve the system using any algebraic method. (7: 10 pts)
Problem 7.
1) 3x + 3y + z = 4
2x – 3y + z = 5
x+y+z=6
2) 2x + 4y + z = 17
3x – 4y + z = -25
x+y+z=4
3) 7x + 2y + z = 7
6x – 2y + z = -16
x+y+z=7
Graph the system of inequalities. (8-11: 6 pts)
Problem 8.
1) x + y > 1
-2x + 3y > -6
2) x + y > 3
-4x + 6y > -12
3) x + y > 4
-8x + 2y > -7
Problem 9.
1) y > 2x – 3
y<3
x > -1
2) y > 4x – 5
y<8
x > -3
3) y > 3x – 7
y<7
x > -5
Problem 10.
1) x + 1 > -1
-6x + y ≥ 1
2) x + 2 > -2
-3x + y ≥ 4
3) x + 3 > -4
-x + y ≥ 2
3
Problem 11.
1) -2x + 3y < 9
10x + 5y > -15
2) -8x + 7y < 21
12x + 3y > -15
3) -3x + 9y < 27
4x + 5y > -16
Evaluate the determinant. (12, 13: 5 pts)
Problem 12.
1) |
1 3
|
−2 2
2) |
3 6
|
−4 2
3) |
1 6
|
−3 7
4) |
15 −3
|
−5 2
Problem 13.
1) |
−3 2
|
4 5
2) |
−3
−14
3) |
−3 −2
|
−4 −5
6
|
4
−3 −12
|
4
−4
Evaluate the determinant. (14-15: 10 pts)
4) |
Problem 14.
5
0
2
1) |−3 9 −1|
1 −4 0
6
1
2) |−4 10
1
0
3
−2|
7
5
2
2
3) |−3 9 −1|
0 −4 3
4
Problem 15.
4 −1 2
1) |−3 −2 −1|
0
5
1
3 −3 4
2) |−5 −4 −3|
0
7
3
4
1
0
3) |−3 −2 −1|
6 −5 1
Extra Credit Problem 1. Solve using any algebraic method:
1) -.03x + .07y + .04z = -.01
0.2x – 0.5y + 0.4z = -4.7
-0.1x + 0.6y + 0.1z = 1.3
2) -.05x + .03y + .09z = 0.22
0.3x – 0.6y + 0.5z = -7.8
-0.3x + 0.4y – 0.8z = 7.1
Extra Credit Problem 2. Graph the system of inequalities:
1) 𝑦 > |𝑥| − 4
𝑦 < −|𝑥| + 4
𝑥 ≥ −2
𝑥≤2
2) 𝑦 > |𝑥 − 2| − 4
𝑦 < −|𝑥 + 3| + 6
𝑥 ≥ −4
𝑥≤7
5