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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

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

7x+10n=1233x+5n=57x=?7x + 10n = 123\\3x + 5n = 57\\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 2y + 6b = 48\\4y + 2b = 46\\y = ?
a A LaTex expression showing 46y = 48
b A LaTex expression showing -90y = 12
c A LaTex expression showing -10y = -10
d A LaTex expression showing -10y = 48
e A LaTex expression showing -90y = -10
f A LaTex expression showing -10y = -90
2
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 2c + 6y = 48\\3c + 3y = 30\\c = ?
a A LaTex expression showing -4c = 48
b A LaTex expression showing 30c = 48
c A LaTex expression showing -4c = -4
d A LaTex expression showing -12c = -4
e A LaTex expression showing -12c = 6
f A LaTex expression showing -4c = -12
3
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 5c + 9m = 65\\2c + 3m = 23\\c = ?
a A LaTex expression showing -1c = -1
b A LaTex expression showing -1c = -4
c A LaTex expression showing -4c = 7
d A LaTex expression showing 23c = 65
e A LaTex expression showing -4c = -1
f A LaTex expression showing -1c = 65
4
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 -2m = 5
c A LaTex expression showing -1m = -1
d A LaTex expression showing 26m = 50
e A LaTex expression showing -1m = 50
f A LaTex expression showing -2m = -1
5
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 -35b = -5
c A LaTex expression showing -35b = 10
d A LaTex expression showing -5b = 147
e A LaTex expression showing -5b = -5
f A LaTex expression showing -5b = -35
6
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 11c + 6p = 40\\8c + 2p = 22\\c = ?
a A LaTex expression showing -13c = -26
b A LaTex expression showing 22c = 40
c A LaTex expression showing -13c = 40
d A LaTex expression showing -13c = -13
e A LaTex expression showing -26c = 5
f A LaTex expression showing -26c = -13
7
Add or subtract multiples of the second equation to the first equation to form a single solvable equation
A LaTex expression showing 7x + 10n = 123\\3x + 5n = 57\\x = ?
a A LaTex expression showing 9x = 1
b A LaTex expression showing 9x = 12
c A LaTex expression showing 1x = 123
d A LaTex expression showing 1x = 1
e A LaTex expression showing 1x = 9
f A LaTex expression showing 57x = 123