Elimination Method to Solve Systems of Equations

Which is the best method for solving this system of equations?

-4x-2y=-12

4x+8y=-24

• Substitution

• Elimination

• Graphing, Not Graphing...

  (aka Picturing the Graph)

  (aka Using graphing skills but not actually graphing)

Which is the best method for solving this system of equations?

x-y=11

2x+y=19

• Elimination

• Substitution

• Graphing, Not Graphing...

  (aka Picturing the Graph)

  (aka Using graphing skills but not actually graphing)

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

• Substitution

• Elimination

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

• Substitution

• Elimination

• Graphing, Not Graphing...

  (aka Picturing the Graph)

  (aka Using graphing skills but not actually graphing)

Solve the system:
3x + y = 19
2x - y = 6

• (5, 14)

• (4, 5)

• (5, 4)

• (14, 5)

7x - y = -10
-7x + 5y = -6

• (-2, -4)

• (-2, -1)

• (-4, -1)

• (6, -8)

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

• 5q + 2z = 1.32
  1z = 0.75

• 5q + 2z = 1.32
  3q + 1z = 0.75

• q + z = 1.32
  q + z = 0.75

• 5q + 2z = 0.75
  3q + 1z = 1.32

What is the first step in solving a system of equations by elimination?

• Rewrite the equations so the variables are all on the same side and line up the like terms.

• Get both equations in slope-intercept form.

• Get both equations equal to zero.

• Put the x terms first.

Answer explanation

We need all of the variables on the same side so that we can eventually add the left side of both equations together and add the right side of both equations together.

If the variables aren't on the same side of the equal-sign, then we can't combine like terms.

To eliminate a variable in the system, should you add the equations or subtract the equations?

• Add

• Subtract

• Neither

Answer explanation

We want to add the equations together in order to eliminate one of the variables. We have opposite terms (3x and -3x) that will "cancel/zero out" (be eliminated) when we add the equations together.

Which variable would be easiest to eliminate?

• x

• y

• Neither

Answer explanation

The terms with x in them have opposite coefficients (4x and -4x), so they will be the easiest to eliminate when we add the equations together.