INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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For more information, please see full course syllabus of Algebra 1

• ## Related Books

 1 answerLast reply by: Dr Carleen EatonWed Jun 19, 2013 11:18 PMPost by Taylor Wright on June 19, 2013Would 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.