Secondary 2 Ch 6 Systems Practice Test
NAME_______________________________ HOUR__________
You must show all of your work to receive credit. ENJOY!!!
Solve each system of equations by graphing it on a calculator. (Round your answer to one decimal place)
1. y = 2x – 3
2. y = -1/3x + 2
3. -8x+4y =2
y = 4/5x + 2
y = 5x - 6
-2x+y =-4
Solve each system using substitution
4.
y = 3x – 4
5.
-x + y = 4
Solve each system using elimination
7. 3x – 4y = 6
x + 4y = 18
a + 3b = 4
2a – 3b = -10
8. a + 3b = 8
-2a – 6b = -16
6.
x – 3y = 5
-2x +6 y = 5
9. x + y = 12
2x – 3y = -11
Solve each system by using a matrix. You must write the resulting matrix to receive full credit
10. x + y = 6
11. 2x - y = 2
12. 2x - y = 2
-2x-2y = 4
-4x +2y = -4
-4x +y = -26
13. x + y + z = 2
2x - y + z = 7
3x + 2y - z = -4
14. -x - y - z = -1
2x +2y +2z = 2
3x +3y+3z= 6
15. x + z = -1
y + z = -3
3x + 2y = 6
Solve each system of equations by graphing it on a calculator. (Round your answer to THREE decimal places)
16. y = -x+2
17. y = x2+2x-5
18. y = -x2-x-4
2
2
y = x +x-6
y = -x +5x + 6
y = x2-3x-3
Solve each non-linear system using either substitution or elimination (SHOW YOUR WORK)
19. y = x-1
20. y = 2x-9
21. (Honors Only)
y = x2-2x-5
y = x2- 6x +3
y = 7x2 -5x-20
y = 2x+22
22.
(HONORS ONLY) Jim has started his own business trimming trees and mowing lawns after school and
on Saturdays. He charges $10/hour trimming trees and $7/hour mowing lawns. He has figured he must
work less than 15 hours a week but he wants to make at least $70 each week. Find all possible solutions to
this problem. (GRAPH IT!) You must write the equations to receive full credit.
Bonus #1: Write YOUR OWN system of equations
that has one solution
Bonus #2: Write YOUR OWN system of equation that
has no solutions
1.)
2.)
3.)
4.)
5.)
6.)
7.)
8.)
9.)
x = 4.2, y = 5.3
x = 1.5, y = 1.5
Ø No Solution
x = 4, y = 8
a = -2, b = 2
Ø No Solutions
x = 6, y = 3
∞ Solutions
x = 5, y = 7
1 1 0
10.) [
] Ø no solutions
0 0 1
1 −.5 1
11.) [
] ∞ Solutions
0 0 0
1 0 12
12.) [
] x = 12, y = 22
0 1 22
13.) x = 1 y = -2 z = 3
14.) No solution
15.) x = 2 y = 0 z = -3
16.) (-4,6) (2,0)
17.) (-1.712, -5.492), (3.212, 11.742)
18.) No solution
19.) (-1,-2), (4,3)
20.) (6,3), (2,-5)
21.) (-2,18), (3,28)
22.) 10x + 7y ≥ 70
x + y < 15
Bonus #1: Two equations that intersect once
Bonus #2: Two equations that never intersect.