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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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Lecture Comments (2)

1 answer

Last reply by: Dr Carleen Eaton
Wed Jun 19, 2013 11:18 PM

Post by Taylor Wright on June 19, 2013

Would it also be possible to multiply either the top or bottom equation by a number (other than 1 or -1) that would allow you to perform the addition/subtraction method?

Solving by Addition and Subtraction

  • If no coefficient is 1 or –1, use the addition and subtraction method. If you can add or subtract the equations and get one variable to vanish, then just solve for the remaining variable. This called elimination.
  • Use this method if the coefficients of one of the variables have the same or opposite signs in the two equations.

Solving by Addition and Subtraction

Solve the system:
2x - 4y = 10
6x + 4y = 14
  • 2x − 4y = 10 + 6x + 4y = 14
  • 2x − 4y = 10 + 6x + 4y = 14 8x = 24
  • x = 3
  • 2x − 4y = 102(3) − 4y = 10
  • 6 − 4y = 10
  • − 4y = 4
y = - 1
Solve the system:
2x + 8y = - 12
16x - 8y = 30
  • 2x + 8y = − 12+ (16x8y = 30)
  • 18x = 18
  • x = 1
  • Plug x back into the equation to find y
  • 2(1) + 8y = − 12
  • 2 + 8y = − 12
  • 8y = − 14
  • y = [( − 14)/8]
y = - [7/4]
8x − 4y = 244x + 4y = 36
  • 8x − 4y = 24 + 4x + 4y = 36
  • 12x = 60
  • x = 5
  • 8x − 4y = 248(5) − 4y = 24
  • 40 − 4y = 24
  • − 4y = − 16
y = 4
12x + 3y = 4811x − 3y = 33
  • 12x + 3y = 48 + 11x3y = 33
  • 22x = 81
x = 3[15/22]
7x − 5y = 177x − 2y = 11
  • 7x − 5y = 17 − 7x2y = 11 − 3y = 6
  • y = − 2
  • 7x − 5y = 177x − 5( − 2) = 17
  • 7x + 10 = 17
  • 7x = 7
x = 1
5x − 6y = 195x − 2y = 11
  • 5x − 6y = 19 − 5x2y = 11
  • 4y = 8
  • y = 2
  • 5x − 6(2) = 19
  • 5x − 12 = 19
  • 5x = 31
x = 6[1/5]
2x − 3y = 182x − 7y = 6
  • 2x − 3y = 18 − 2x7y = 6
  • 10y = 12
  • y = [12/10] = [6/5]
  • y = 1[1/5]
  • 2x − 3( 1[1/5] ) = 18
  • 2x − 3[3/5] = 18
  • 2x = 21[3/5]
x = 10[4/5]
x − 5y = 177x − 2y = 11
  • 7x − 5y = 17 − 7x2y = 11 − 3y = 6
  • y = − 2
  • 7x − 5y = 177x − 5( − 2) = 17
  • 7x + 10 = 17
  • 7x = 7
x = 1
5x − 6y = 195x − 2y = 11
  • 5x − 6y = 19 − 5x2y = 11
  • 4y = 8
  • y = 2
  • 5x − 6(2) = 19
  • 5x − 12 = 19
  • 5x = 31
x = 6[1/5]
2x − 3y = 182x − 7y = 6
  • 2x − 3y = 18 − 2x7y = 6
  • 10y = 12
  • y = [12/10] = [6/5]
  • y = 1[1/5]
  • 2x − 3( 1[1/5] ) = 18
  • 2x − 3[3/5] = 18
  • 2x = 21[3/5]
x = 10[4/5]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Solving by Addition and Subtraction

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Fundamental Principle 0:10
    • Example
  • Example 1: Solve the System 1:52
  • Example 2: Solve the System 5:53
  • Example 3: Solve the System 10:15
  • Example 4: Solve the System 14:08