Download Systems of Equations Study Guide

Gautier/Tang
Algebra I: Ch. 9-4 & 9-5
Name __________________________
Date ___________
Chapter 9 Study Guide: Systems of Equations
QUIZ: Wednesday 11/29/06
Sec. 9-4 The Addition-or-Subtraction Method
5x – y = 12
3x + y = 4
Solve
5x – y = 12
3x + y = 4
8x
= 16
1. Add similar terms of the two equations.
2. Solve the resulting equation.
x=2
3. Substitute 2 for x in either of the original
equations to find y.
3x + y = 4
3(2) + y = 4
6+y=4
6+y=4
-6
-6
Solve for y
y = -2
Check x = 2 and y = -2 in both original equations.
3x + y = 4
5x – y = 12
3(2) + -2 = 4
5(2) – (-2) = 12
4 = 4 Correct
12 = 12 Correct
* If you are using subtraction because none of the terms cancel each
other out, CHANGE ALL THE SIGNS IN THAT EQUATION FIRST*
Ex:
8x + 10y = 42 
rewrite
 8x + 10y = 42
8x + 24y = 10  change the signs to subtract  -8x – 24y = -10
1
Gautier/Tang
Algebra I: Ch. 9-4 & 9-5
Practice Problems
Solve by using the addition or subtraction method.
1. 3x + 2y = 7
-5x – 2y = 1
5. 6p – 7q = 28
-6p + 3q = -12
2. 2c + 3d = 0
5c – 3d = 21
6. 3p + 2q = 19
3p – 5q = 5
3. –3x + 5y = 45
3x + 13y = 9
7. 6c + 7d = -15
6c – 2d = 12
4. 12p – 18q = 14
-15p – 18q = -4
8. –4s + 7t = 10
4s – 2t = 5
2
Gautier/Tang
Algebra I: Ch. 9-4 & 9-5
Sec. 9-5 Multiplication with the Addition-or-Subtraction Method
* You must multiply the equation(s) so that terms with the same
variable have the SAME COEFFICIENT, and OPPOSITE SIGNS.*
Example:
Solve 4x – 5y = 23
3x + 10y = 31
2[4x – 5y = 23]
3x + 10y = 31
= 8x – 10y = 46
3x + 10y = 31
8x – 10y = 46
3x + 10y = 31
11x
= 77
11x 77

11 11
Multiply the top equation by 2 so that the y
terms are equal and opposite.
Rewrite both equations to solve.
Add similar terms and solve the equation.
x=7
TO FIND y:
4(7) – 5y = 23
Substitute 7 for x in either original equation
to find the value of y.
28 – 5y = 23
-28
-28
-5y = -5
-5
-5
y=1
CHECK in both original equations:
4x – 5y = 23
4(7) – 5(1) = 23 ?
28 – 5 = 23 √
3x + 10y = 31
3(7) + 10(1) = 31 ?
21 + 10 = 31 √
3
Gautier/Tang
Algebra I: Ch. 9-4 & 9-5
Practice Problems
Solve each system using multiplication with the addition-or-subtraction
method.
1. 4x + 15t = 10
3x + 10t = 5
5. 4r + 9s = 23
-7r + 3s = -34
2. 18a – 5b = 17
6a + 10b = -6
6. 3t – 8z = 34
7t + 4z = -34
3. 3p + 8q = 8
5p – 2q = 21
7. 3c – 8d = 7
c + 2d = -7
4. 6n + 8c – 4 = 0
9n + 10c – 7 = 0
8. 3p + 4q = 4
5p + 2q = 16
4