Solving Systems of Linear Equations Using Elimination

Solve the system of equations.
y = 4x+1
3x + 2y = 13

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

a method to solving a system of equations by getting rid of one of the variables first to solve for the other variable. 

• Systems by Graphing

• Systems by Substitution

• Systems by Elimination

• Systems by Drawing

Solve the system by elimination. 7x - y = -10 -7x + 5y = -6

• (-2, -4)

• (-2, -1)

• (-4, -1)

• (6, -8)

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450

• Add the x terms in the two equations and the y terms in the two equations so you get 3x + 8y = 11

• Multiply all terms in the top equation by 2 so that you  can eliminate the x terms

• Multiply the x in the first equation by -2 so you get -2x + y = 2

• Multiply all terms in the top equation by -2 so that you can eliminate the x terms. 

• (-2,2)

• (2,-2)

• (-2,-2)

• (-2, 1/2)

Describe the error in solving the system of equations using elimination:

• They eliminated the x terms when they should have eliminated the y terms.

• The subtracted 5x and x to get 4x, but they should have added the x terms to get 6x = 24.

• They added 16 and 8 to get 24, but they should have subtracted them to get 8 on the right side of the equation.

• They eliminated the y terms, but they couldn't because one is a negative and one is a positive.

• (16,19)

• (19,-16)

• (-19,-16)

• (19,16)

• -1

• 6

• 1

• -6

Which of the following is the correct solution to the system of linear equations?

• (6, 10/3)

• (6,5)

• (4,5)

• (4,-5)