Systems Elimination Strategy

After you eliminate the x variables, you can solve for y.  Do it! What do you get?

Once you find that y = -6, you can plug -6 in for y into either equation. Once you do this, simplify and solve for x. What do you get?

• x = 0

To eliminate the x variables

• multiple the top equation by -1

• multiply the bottom equation by 4

• multiply the bottom equation by -4

• multiply the bottom equation by -1

To eliminate the y variable, . . .

• subtract the equations

• add the equations

• multiply the bottom equation by -1 and then add the equations together

Solve the system by elimination. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 

• Infinite number of solutions  

• (−6, 10) 

• (6, 4) 

Solve the system by elimination.  

4x + 12y = −1
−3x − 9y = 0 

• (10, 1) 

• (−10, −1) 

•  (10, −1) 

•  No solution 

Josh is thinking of two numbers.  Their sum is -10 and their difference is -2.  Which system of equations represents the situation?

• x - y = -10
  x + y = -2

• x = -2 
  y = 5

• x + y = -2
  x - y = -10

• x + y = -10
  x - y = -2

Flagship Cinemas sells movie tickets that are $4 for matinees and $7 for regular. One night, the theater sells 578 tickets and collects $3365 in total ticket sales.
Which system best represents the situation?

• 4x + 7y = 578
  x + y = 3365

• 4x + 7y = 3365
  x + y = 578

• 4y + 7x = 578
  x + y = 3365

• 4y + 7x = 3365
  x + y = 578

Systems by Elimination

3) x = ___

Which method would be best (quickest) for solving the system below: x + y = 11 3x - 4y = -2

• Making trials

• Elimination

• Graphing

• None of these