Study Guide: Elimination Using Addition and Subtraction

These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 textbook (Glencoe Algebra 1 — ISBN: 9780028253282) into html format.

Study Guide
Elimination Using Addition and Subtraction

In systems of equations where the coefficient of the y or y terms are additive inverses, solve the system by adding the equations. Because one of the variables is eliminated, this method is called eliminationOne method of solving systems of equations is by algebraic substitution.

Example: Use elimination to solve the systems of equations x − 3y = 7 and 3x + 3y = 9.

Sometimes the equations are presented with the following notation:

{	x − 3y = 7 3x + 3y = 9

where the { shows that the equations form a system.

Directions: Use elimination to solve each system of equations.

(2, −3)

(−1, 2)

(6, 0)

Directions: Use a system of equations and elimination to solve each problem.

7. Two angles are supplementary. The measure of one angle is 10 more than three times the other. Find the measure of each angle.

42.5°, 137.5°

8. Remo is older than Ken. The difference of their age is 12 and the sum of their ages is 50. Find the age of each.

Rema is 31; Ken is 19

9. The sum of two numbers is 70 and their difference is 24. Find the two numbers.

23 and 47

10. The sum of the digits of a two-digit number is 12. The difference in the digits is 2. Find the number if the units digit is larger than the tens digit.