AFDA
Solving Systems of Equations Review
1
Key Questions:
- Did you get a value for x or y? Plug this value into one of original equations and solve for
the other variable. Your system has one solution. Write it as an ordered pair.
- Did you eliminate both variables and get a true statement? Your system has many solutions
- Did you eliminate both variables and get a false statement? Your system has no solution
Questions 1-6: Solve the systems using the substitution method.
* Remember: Solve one of the equations for x OR y. LOOK: One of the equations may already
be solved. Substitute this expression into the other equation. Solve for the variable. Substitute
this value into one of original equations to solve for the other variable. Put x & y together as an
ordered pair; this is your solution.
3x  4 y  6

y  x 1
2.
x  y  3

2 x  y  1
 y  2 x  12
3. 
4 x  2 y  144
4.
x  3y

 x  5 y  16
1.
5.
4 x  3 y  8

 x  2 y  13
2 x  y  2
6. 
 y  x  1
AFDA
Solving Systems of Equations Review
2
Questions 7-12: Solve the systems using the elimination method.
* Remember: your goal is to eliminate a variable. To do so, you must have the same number,
different signs. You may need to multiply ONE or BOTH of the equations. Once a variable is
eliminated, combine remaining and solve. Plug this answer into one of the original equations to
solve for the other variable. Put x & y together as an ordered pair for your solution.
2 x  5 y  14
7. 
6 x  7 y  10
3x  4 y  8
8. 
x  2 y  4
3x  y  6
9. 
 3x  4 y  9
 2 x  5 y  12
10. 
6 x  15 y  36
4 x  5 y  7
11. 
6 x  2 y  18
5 x  2 y  5
12. 
3x  y  2
AFDA
Solving Systems of Equations Review
3
Questions 13-16: Graph the following linear systems.
* Remember: Graph each equation in the coordinate plane. Equation must be in slope intercept
form FIRST (y=mx + b). Identify the point of intersection of the lines. This is the solution;
write is as an ordered pair.
* Intersecting lines: One solution * Parallel Lines: No solution * Same Line: Many Solutions
13.
 y  12 x  3

 y  x  4
14.
Solution: ____________
 y  3x  1

 y  3x  4
Solution: ____________
y
y
x
x
2 x  y  5
15. 
x  y  1
2 y  x  2
16. 
 2 x  4 y  4
Solution: ____________
Solution: ____________
y
y
x
x
AFDA
Solving Systems of Equations Review
4
Questions 17-20: Solve the following system of equations, using any method.
3x  9 y  0
17. 
 x  3 y  3
3x  y  9
18. 
6 x  2 y  10
y  9  x
19. 
 x  3 y  3
4 x  4 y  8
20. 
2 x  2 y  4
Questions 21-22: Determine whether or not the ordered pair is a solution to the given system.
Support your answer mathematically.
21.
Plug in x & y to both equations in the system. Do you get a true statement for BOTH?
4 x  4 y  4

 2 x  y  2
(-3, -4)
22.
3x  5 y  9

 x  2 y  8
(4, 6)
AFDA
Solving Systems of Equations Review
5
Question 23-26: Set up a system of equations for each situation and solve appropriately
Remember: All money together in one equation!
23.
The sum of two numbers is 90. Their difference is 18. What are the two numbers?
24.
A math teacher  bought rulers and scissors for her classroom. She bought a total of 15
items. The rulers cost $0.59 each and the scissors were $2.12 each. If she spent $18.03
total how many of each did she buy?
25.
You and your friends are throwing an end of the school year cookout. You need to buy 8
packages of meat. A package of hotdogs cost $1.60 and a package of hamburger costs
$5.00. If you spend a total of $23.00, how many packages of each did you buy?
26.
Tickets to a concert are $5 for balcony seats and $10 for floor seats. If 600 people
attended and $4750 was collected, how many people sat in each type of seat?