Intermediate Algebra
Chapter 9 Review
9.1 Solutions of Systems of Equations and Solving by Graphing
Determine whether the given ordered pair is a solution of the system.
1. (5,3)
2. (2, -2)
2x – y = 7
9x + 4y = 10
y = 3x – 8
x+y=2
Solve each system by graphing.
1. 2x + y = 1
2. 2x – 2y = 2
3. 3y + 2x = 6
y–x=4
x– y=1
2x + 3y = 0
9.2 Solving Systems of Equation by Substitution
1. Solve the equation for one of the variables.
2. Substitute this expression in the other equation and solve for the other
variable.
3. Substitute this value in the equation in Step 1 and solve.
Solve by the substitution method:
1.
y = -x + 15
4x + 3y = 38
2.
2x + y = -2
4x + 5 = -2y
9.4 & 9.5 Solving Systems of Equation by Elimination
Solve by the elimination method.
1. 5x – y = 12
3x + y = 4
3.
x – y = 11
3x + 10y = -6
2. 5x – 3y = 10
x – 3y = 2
4. 2y + 5x = 14
6y + 7x = 10
Word Problems Using Systems
Step 1: Read the problem and define the variables.
Step 2: Write 2 equations from the information in the problem.
Step 3: Solve the system of equations using one of the methods. (graph,
sub, elim)
Step 4: Check and label the answer.
1. The sum of two numbers is 29 and their difference is 5. Find the two numbers.
Variable Definition
Equations
Labeled Answer
2. Shannyn bought a total of 7 postcards for $1.80. If the small postcards cost 20 cents each and
the large postcards cost 30 cents each, how many postcards o each size did he buy?
Variable Definition
Equations
Labeled Answer