Linear Equations by Elimination

Should you use the Substitution or Elimination method to solve this system of equations?

• Substitution

• Elimination

What is the purpose of multiplying the equations in the elimination method?

• To waste time and effort

• To confuse the person solving the equations

• To make the equations look more complicated

• To create opposite coefficients for one of the variables

Solve by elimination:
9x-4y=7

x-4y=-17

• (-1,5)

• (-7,5)

• (7,5)

• (3,5)

Solve by elimination:
3x+7y=23

-3x-7y=-17

• No solution

• ARN

• (-3,3)

• (3,3)

Solve by elimination
4x-6y= -6
-2x-12y= -12

• (0,1) 

• (1,0)

• (1,1)

• (2,1)

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740

• S + A = 530
  4S + 3A = 1740

• S + A = 1740
  3S + 4A = 530

• S + A = 1740
  4S + 3A = 530

Solve by elimination
-12x-10y= 0
6x+5y= -1

• infinite solutions

• (0,0)

• no solution

• (2,1)

Solve by elimination 
-6x+y= -2
-3x-6y= 12

• (2,0)

• no solution 

• (0,-2)

• infinite solutions 

Solve using elimination. 
−4x − 4y = 0
  8x + 8y = 0 

• (−6, −4) 

• Infinite number of solutions  

• No solutions

• (6, 4) 

Solve the system by elimination.
     4x + 12y = −1
−3x − 9y = 0 

• (10, 1) 

• (−10, −1) 

• (10, −1) 

• No solution