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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Math worksheet on 'Linear Equation Systems - Simple Addition To Equation (Level 3)'. Part of a broader unit on 'Algebra Systems of Equations - Intro' Learn online: app.mobius.academy/math/units/algebra_systems_of_equations_intro/
1
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 18z = 12
b A LaTex expression showing 2z = 18
c A LaTex expression showing 2z = 130
d A LaTex expression showing 18z = 2
e A LaTex expression showing 2z = 2
f A LaTex expression showing 56z = 130
2
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 11r + 6m = 153\\2r + 3m = 45\\r = ?
a A LaTex expression showing 7r = 153
b A LaTex expression showing 7r = 63
c A LaTex expression showing 63r = 7
d A LaTex expression showing 63r = 12
e A LaTex expression showing 7r = 7
f A LaTex expression showing 45r = 153
3
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 12r + 9p = 69\\9r + 3p = 33\\r = ?
a A LaTex expression showing -15r = -30
b A LaTex expression showing -30r = -15
c A LaTex expression showing -15r = -15
d A LaTex expression showing 33r = 69
e A LaTex expression showing -30r = 5
f A LaTex expression showing -15r = 69
4
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 12b + 6m = 138\\6b + 2m = 60\\b = ?
a A LaTex expression showing -6b = 138
b A LaTex expression showing -6b = -42
c A LaTex expression showing 60b = 138
d A LaTex expression showing -42b = -6
e A LaTex expression showing -6b = -6
f A LaTex expression showing -42b = 10
5
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 7m + 6r = 50\\4m + 3r = 26\\m = ?
a A LaTex expression showing -1m = -2
b A LaTex expression showing 26m = 50
c A LaTex expression showing -2m = -1
d A LaTex expression showing -1m = -1
e A LaTex expression showing -2m = 5
f A LaTex expression showing -1m = 50
6
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 8r + 4m = 44\\10r + 2m = 46\\r = ?
a A LaTex expression showing -48r = 7
b A LaTex expression showing -48r = -12
c A LaTex expression showing -12r = 44
d A LaTex expression showing -12r = -48
e A LaTex expression showing 46r = 44
f A LaTex expression showing -12r = -12
7
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 91b = 147
b A LaTex expression showing -5b = 147
c A LaTex expression showing -35b = 10
d A LaTex expression showing -5b = -5
e A LaTex expression showing -5b = -35
f A LaTex expression showing -35b = -5
Linear Equation Systems - Simple Addition To Equation (Level 3) - Mobius Math