This math topic focuses on solving systems of linear equations by adding or subtracting multiples of one equation to another to create a single, solvable equation. It addresses introductory algebra concepts related to manipulating equations to isolate variables and find solutions. Each problem presents a pair of simultaneous equations with specific instructions to combine them, streamlining the system into one equation that can be solved for the variable of interest. The issues also provide multiple possible numerical answers to reinforce the concept of checking solutions within the context of linear equations.

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Linear Equation Systems - Simple Addition To Equation Worksheet

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Linear Equation Systems - Simple Addition To Equation
1
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 6x + 3d = 33\\5x - 3d = 0\\x = ?
a A LaTex expression showing 33x = 6
b A LaTex expression showing 0x = 33
c A LaTex expression showing 11x = 11
d A LaTex expression showing 11x = 33
e A LaTex expression showing 33x = 11
f A LaTex expression showing 0x - 3x + 2 = 33
2
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 9p + 12r = 105\\5p - 12r = -35\\p = ?
a A LaTex expression showing 70p = 14
b A LaTex expression showing 70p = 8
c A LaTex expression showing -35p = 105
d A LaTex expression showing 14p = 105
e A LaTex expression showing 14p = 70
f A LaTex expression showing 14p = 14
3
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 8x + 4c = 60\\2x - 4c = -20\\x = ?
a A LaTex expression showing 10x = 40
b A LaTex expression showing 10x = 10
c A LaTex expression showing 10x = 60
d A LaTex expression showing 40x = 7
e A LaTex expression showing 40x = 10
f A LaTex expression showing -20x = 60
4
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 8y + 5m = 117\\-8y + 9m = 9\\m = ?
a A LaTex expression showing 126m = 14
b A LaTex expression showing 14m = 126
c A LaTex expression showing 9m = 117
d A LaTex expression showing 126m = 12
e A LaTex expression showing 14m = 14
f A LaTex expression showing 14m = 117
5
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 12c + 12p = 120\\8c - 12p = -80\\c = ?
a A LaTex expression showing 20c = 40
b A LaTex expression showing 40c = 5
c A LaTex expression showing 40c = 20
d A LaTex expression showing 20c = 20
e A LaTex expression showing 20c = 120
f A LaTex expression showing -80c = 120
6
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 9r + 10n = 74\\-9r + 4n = -46\\n = ?
a A LaTex expression showing 14n = 28
b A LaTex expression showing 14n = 14
c A LaTex expression showing -46n = 74
d A LaTex expression showing 28n = 5
e A LaTex expression showing 14n = 74
f A LaTex expression showing 28n = 14
7
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 5b + 9m = 69\\-5b + 6m = 21\\m = ?
a A LaTex expression showing 90m = 15
b A LaTex expression showing 15m = 90
c A LaTex expression showing 15m = 69
d A LaTex expression showing 15m = 15
e A LaTex expression showing 21m = 69
f A LaTex expression showing 90m = 9
8
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 10r + 6m = 78\\8r - 6m = 30\\r = ?
a A LaTex expression showing 18r = 78
b A LaTex expression showing 108r = 18
c A LaTex expression showing 30r = 78
d A LaTex expression showing 18r = 108
e A LaTex expression showing 108r = 9
f A LaTex expression showing 18r = 18