This math topic focuses on manipulating linear equation systems through addition or subtraction of multiples of one equation to another to simplify the system into a single solvable equation. It is designed to enhance skills in algebraic manipulation and solving linear systems of equations. Each problem presents a set of two equations with variables and constants, and the task involves combining these equations strategically to isolate one variable. This skill is fundamental in algebra, particularly useful in deriving values from systems of equations in more advanced mathematical contexts.

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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 11z + 8m = 82\\3z + 4m = 26\\z = ?
a A LaTex expression showing 5z = 5
b A LaTex expression showing 30z = 5
c A LaTex expression showing 30z = 9
d A LaTex expression showing 5z = 30
e A LaTex expression showing 5z = 82
f A LaTex expression showing 26z = 82
2
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 5c + 6n = 69\\10c + 3n = 102\\c = ?
a A LaTex expression showing -135c = -15
b A LaTex expression showing 102c = 69
c A LaTex expression showing -15c = 69
d A LaTex expression showing -15c = -135
e A LaTex expression showing -15c = -15
f A LaTex expression showing -135c = 12
3
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 9d + 8p = 95\\10d + 4p = 86\\d = ?
a A LaTex expression showing 86d = 95
b A LaTex expression showing -11d = 95
c A LaTex expression showing -11d = -77
d A LaTex expression showing -77d = -11
e A LaTex expression showing -11d = -11
f A LaTex expression showing -77d = 10
4
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 9b + 12d = 147\\7b + 6d = 91\\b = ?
a A LaTex expression showing -5b = -5
b A LaTex expression showing 91b = 147
c A LaTex expression showing -35b = -5
d A LaTex expression showing -35b = 10
e A LaTex expression showing -5b = -35
f A LaTex expression showing -5b = 147
5
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 4d + 8x = 44\\7d + 4x = 57\\d = ?
a A LaTex expression showing -10d = -10
b A LaTex expression showing -70d = -10
c A LaTex expression showing 57d = 44
d A LaTex expression showing -10d = 44
e A LaTex expression showing -10d = -70
f A LaTex expression showing -70d = 10
6
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 2b + 9r = 73\\3b + 3r = 36\\b = ?
a A LaTex expression showing -7b = 73
b A LaTex expression showing 36b = 73
c A LaTex expression showing -35b = 8
d A LaTex expression showing -35b = -7
e A LaTex expression showing -7b = -7
f A LaTex expression showing -7b = -35
7
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 12c + 6b = 72\\6c + 2b = 30\\c = ?
a A LaTex expression showing -18c = 6
b A LaTex expression showing -18c = -6
c A LaTex expression showing -6c = -6
d A LaTex expression showing -6c = -18
e A LaTex expression showing 30c = 72
f A LaTex expression showing -6c = 72
8
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 10z + 8d = 130\\4z + 4d = 56\\z = ?
a A LaTex expression showing 56z = 130
b A LaTex expression showing 18z = 12
c A LaTex expression showing 18z = 2
d A LaTex expression showing 2z = 130
e A LaTex expression showing 2z = 2
f A LaTex expression showing 2z = 18