M317 – Algebra II
Chapter 3
Worksheet 4
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Date______________ Period______
Teacher_______________________
Determine whether the given point is a solution to the system of equations.
1. Is (1,5) a solution?
2. Is ( 2, 6) a solution?
3x  y  2
y  3x
4 x  2 y  5
x  2 y  14
3. Is (4, 7) a solution?
x4
y  7
Solve each linear system by graphing.
Declare how many solutions exist (one, infinite, or none). If one solution exists state the exact solution.
Describe each system as consistent/inconsistent and dependent/independent.
4.
2x  y  4
5.
x y 2
Number of solutions:
One ________
x y 2
x y 6
Number of solutions:
None
Infinite
Describe the solutions:
consistent / inconsistent
One ________
None
Infinite
Describe the solutions:
dependent / independent
consistent / inconsistent
6. How many solutions do parallel lines have?
7. How many solutions do two lines with the same equation have?
8. How many solutions do two lines that intersect at one point have?
dependent / independent
Use substitution to solve each system of equations.
9.
2x  y  4
3x  2 y  1
10.
x  9  3y
x  2 y  1
Use elimination (linear combinations) to solve each system of equations.
11.
2x  y  1
3x  y  14
12.
2 x  y  1
3 x  2 y  30
Use any method to solve each system of equations.
13.
8x  3 y  5  0
10 x  13  6 y
2
3
x  y  2
5
4
14.
1
1
x y 7
2
4
15.
3 x  4 y  12
6 x  2 y  11
16.
4x  3y  3
2 x  y  3
1
x y 9
17. 2
3x  3 y  12
2 x  y  2 z  15
18.  x  y  z  3
3 x  y  2 z  18
2a  5b  c  5
19. c  3a  17  2b
3b  4a  17  2c
p  4 r  7
20.
p  3q  8
q  r 1
Solve each system of inequalities by graphing.
21.
y4
y  x3
x  2
1
x2
2
3y  4x  9
22. y 