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Linear Equation Systems - Simple Addition To Equation (Level 2)

This math topic focuses on solving systems of linear equations by eliminating variables through the addition or subtraction of multiples of one equation to another. It is intended for beginners learning about algebraic methods to solve for unknown variables in a system of equations. Each problem presents a pair of equations with two variables and asks to simplify them into a single equation by strategically combining them. The aim is to isolate one variable and solve for it, enhancing skills in manipulation of equations and understanding the relationships between variables in linear systems.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Linear Equation Systems - Simple Addition To Equation

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

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

3n+10y=322n−5y=−2n=?3n + 10y = 32\\2n - 5y = -2\\n = ?

Linear Equation Systems - Simple Addition To Equation Worksheet

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Math worksheet on 'Linear Equation Systems - Simple Addition To Equation (Level 2)'. 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 4p + 4n = 28\\-2p + 5n = 0\\n = ?
a A LaTex expression showing 28n = 14
b A LaTex expression showing 0n = 28
c A LaTex expression showing 14n = 28
d A LaTex expression showing 4n + 0n - 14 = 28
e A LaTex expression showing 28n = 5
f A LaTex expression showing 14n = 14
2
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 8r + 3d = 55\\-4r + 2d = -10\\d = ?
a A LaTex expression showing 7d = 35
b A LaTex expression showing 7d = 55
c A LaTex expression showing -10d = 55
d A LaTex expression showing 7d = 7
e A LaTex expression showing 35d = 7
f A LaTex expression showing 35d = 8
3
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 12n + 2p = 86\\-6n + 4p = -8\\p = ?
a A LaTex expression showing 70p = 10
b A LaTex expression showing -8p = 86
c A LaTex expression showing 70p = 10
d A LaTex expression showing 10p = 70
e A LaTex expression showing 10p = 10
f A LaTex expression showing 10p = 86
4
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 8n + 3p = 71\\-4n + 6p = 2\\p = ?
a A LaTex expression showing 15p = 15
b A LaTex expression showing 15p = 75
c A LaTex expression showing 15p = 71
d A LaTex expression showing 2p = 71
e A LaTex expression showing 75p = 8
f A LaTex expression showing 75p = 15
5
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 2x + 12m = 124\\3x - 6m = -30\\x = ?
a A LaTex expression showing 64x = 8
b A LaTex expression showing 64x = 11
c A LaTex expression showing 8x = 124
d A LaTex expression showing 8x = 8
e A LaTex expression showing 8x = 64
f A LaTex expression showing -30x = 124
6
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 2y + 6n = 52\\4y - 3n = -16\\y = ?
a A LaTex expression showing 10y = 10
b A LaTex expression showing 20y = 10
c A LaTex expression showing -16y = 52
d A LaTex expression showing 10y = 52
e A LaTex expression showing 20y = 5
f A LaTex expression showing 10y = 20
7
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 6c + 2y = 16\\-3c + 3y = 0\\y = ?
a A LaTex expression showing 8y = 8
b A LaTex expression showing 0y = 16
c A LaTex expression showing 16y = 5
d A LaTex expression showing 16y = 8
e A LaTex expression showing 8y = 16
f A LaTex expression showing 2y + 0y - 8 = 16