Systems Elimination and Word Problems

Systems by Elimination

Math 1 January 5, 2021

Systems by Elimination

You have already developed some useful strategies for solving a simple linear equation like 3x + 5 = 10. You know that you can add or subtract the same quantity on both sides and preserve equality. The same is true for multiplication or division. These ideas, called the Properties of Equality, can help you develop another method for solving linear equations. This method involves combining separate linear equations (through the four basic operations) into one equation with only one variable. Other names for this method are Combination, Addition, or Elimination.

Example 1

 $x+y=3$  
 $x-y=9$  

Example 2

 $2x-4y=10$  
 $-2x+6y=-4$  

Example 3

 $6x-7y=-4$  
 $-4x-7y=26$  

Example 4

 $x+3y=9$  
 $x-2y=-6$  

Example 5

 $2x+5y=-1$  
 $x+2y=0$  

Example 6

 $6x+3y=0$  
 $-3x+3y=9$