Name_________________________
Algebra II Chapter 3 Review
No Calculator Section
Solve the following systems of equations by graphing.
1)
3)
3x  4y  8
2y  x  6
2)
3x  2y 10
4x  y  6
When would a system with two equations have no solution?
Solve the systems of equations by substitution.
4)
2x  y  4
5)
3x  2y 1
x  3y  7
3x  y 1
Solve the systems of equations by elimination.
6)
2
1
x  y 15
3
3
6x  2y 10
7)
2x  y
7
3
3x  y  9
Solve the systems of equations by substitution or elimination.
8)
8x  3y   5
6y  10x  13  0
9)
9x  y  30
6x 15  y
Solve each system by graphing.
10) y  4  x
y   3x  1
12) y  x  2  3
y x 2
11) y  3 x
x  y2
13) x  2y  6
y x 3
Calculator Section
Solve the systems of equations.
14) 2x  y  z 1
16)
15) x  2y  z   3
x y 5
x  y  z  1
2x   6
2x  4y  z 1
17)
Write & solve a system of equations.
18) The sum of three numbers is 6. The third number is
the sum of the first and second numbers. The first
number is one more than the third number. Find the
numbers.
19) Alissa, Jake, and Dylan are siblings. They have lived a
total of 61 years combined. Alissa has lived two more
years than Dylan. Jake and Dylan combined have lived
17 years longer than Alissa. Find the age of each
sibling.
20) Meg, Katy, and Chris are keeping track of how far they run each day. At the end of the week, they combined their
distances and found that they ran 82 miles in total. Katy ran twice as far as Meg, and Chris ran 2 more miles than
Meg. How far did each person run?
Answers
1. (4, -1)
11.
2. (2, -2)
12.
3.
4.
5.
6.
7.
Same slope / parallel lines
(7, -10)
(1, -2)
(10, 25)
(6, 9)
13. y 
8.
1

 , 3 
2

9. (3, 3)
10.
14.
15.
16.
17.
18.
19.
20.
1
x 3
2
(-3, -2, -5)
(-20, 12, 7)
(-2, -3, 1)
(15, -1, 5)
(4, -1, 3)
A=22, D=20, J=19
C=22, K=40, M=20