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Elementary and Intermediate Algebra
Mark Dugopolski, Southeastern Louisiana University
Systems of Linear Equations and Inequalities
The Addition Method

Warm-Ups



1

Exercises 1–6 refer to the following systems.

a)  3x - y = 9 b)  4x - 2y = 20 c)  x - y = 6
2x + y = 6 -2x + y = -10 x - y = 7

To solve system (a) by addition, we simply add the equations.
A)TRUE
B)FALSE
2

To solve system (a) by addition, we can multiply the first equation by 2 and the second by 3 and then add.
A)TRUE
B)FALSE
3

To solve system (b) by addition, we can multiply the second equation by 2 and then add.
A)TRUE
B)FALSE
4

Both (0, -10) and (5, 0) are in the solution set to system (b).
A)TRUE
B)FALSE
5

The solution set to system (b) is the set of all real numbers.
A)TRUE
B)FALSE
6

System (c) has no solution.
A)TRUE
B)FALSE
7

Both the addition method and substitution method are used to eliminate a variable from a system of two linear equations in two variables.
A)TRUE
B)FALSE
8

For the addition method, both equations must be in standard form.
A)TRUE
B)FALSE
9

To eliminate fractions in an equation, we multiply each side by the least common denominator of all fractions involved.
A)TRUE
B)FALSE
10

We can eliminate either variable by using the addition method.
A)TRUE
B)FALSE








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