Linear Equation Systems - Simple Addition To Equation (Level 3)

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

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Add or subtract multiples of the second equation to the first equation to form a single solvable equation

12x+10y=1423x+2y=32x=?12x + 10y = 142\\3x + 2y = 32\\x = ?

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 5c + 6n = 69\\10c + 3n = 102\\c = ?
a A LaTex expression showing -15c = -15
b A LaTex expression showing 102c = 69
c A LaTex expression showing -15c = -135
d A LaTex expression showing -135c = 12
e A LaTex expression showing -15c = 69
f A LaTex expression showing -135c = -15
2
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 12r + 8d = 88\\3r + 2d = 22\\r = ?
a A LaTex expression showing 12r + 22r - 0 = 88
b A LaTex expression showing 0r = 0
c A LaTex expression showing 0r = 88
d A LaTex expression showing 22r - 8r + 5 = 88
e A LaTex expression showing 0r = 9
f A LaTex expression showing 22r = 88
3
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 30c = 72
b A LaTex expression showing -18c = 6
c A LaTex expression showing -6c = 72
d A LaTex expression showing -6c = -6
e A LaTex expression showing -6c = -18
f A LaTex expression showing -18c = -6
4
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 11z + 10m = 52\\12z + 5m = 39\\z = ?
a A LaTex expression showing -13z = -26
b A LaTex expression showing -13z = -13
c A LaTex expression showing -13z = 52
d A LaTex expression showing 39z = 52
e A LaTex expression showing -26z = 5
f A LaTex expression showing -26z = -13
5
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 12z + 12b = 96\\3z + 4b = 26\\z = ?
a A LaTex expression showing 18z = 3
b A LaTex expression showing 3z = 3
c A LaTex expression showing 26z = 96
d A LaTex expression showing 18z = 9
e A LaTex expression showing 3z = 96
f A LaTex expression showing 3z = 18
6
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 8p + 12m = 56\\5p + 6m = 32\\p = ?
a A LaTex expression showing -2p = -2
b A LaTex expression showing -8p = -2
c A LaTex expression showing -2p = 56
d A LaTex expression showing 32p = 56
e A LaTex expression showing -2p = -8
f A LaTex expression showing -8p = 7
7
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 6d + 4z = 56\\2d + 2z = 20\\d = ?
a A LaTex expression showing 2d = 56
b A LaTex expression showing 20d = 56
c A LaTex expression showing 2d = 2
d A LaTex expression showing 2d = 16
e A LaTex expression showing 16d = 2
f A LaTex expression showing 16d = 11