Linear Equation Systems - Simple Variable Substitution To Equation

Level 1

This math topic focuses on solving systems of linear equations through the method of variable substitution, aimed at beginners. Each question presents a system with two equations where students must substitute one variable equation into the other to form a single solvable equation. The student's task is to simplify these equations and solve for the unknown variables, enhancing their algebraic manipulation and equation solving skills. This set of problems is part of a broader introduction to algebraic systems of equations.

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

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Linear Equation Systems - Simple Variable Substitution To Equation

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


Substitute the second variable equation into the first equation to form a single solvable equation

6c+y=54y=3cc=?6c + y = 54\\y = 3c\\c = ?

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Linear Equation Systems - Simple Variable Substitution To Equation Worksheet

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Math worksheet on 'Linear Equation Systems - Simple Variable Substitution To Equation (Level 1)'. Part of a broader unit on 'Algebra Systems of Equations - Intro' Learn online: app.mobius.academy/math/units/algebra_systems_of_equations_intro/
1
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 12c + m = 100\\m = 8c\\c = ?
a A LaTex expression showing 12c - 7c = 100
b A LaTex expression showing 12c + 8c = 100
c A LaTex expression showing 12c + 8 = 100
d A LaTex expression showing 12c + 6c = 100
e A LaTex expression showing 8c + 8 = c
f A LaTex expression showing 12c + 7c = 100
2
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 11x + d = 105\\d = 4x\\x = ?
a A LaTex expression showing 11x + 4 = 105
b A LaTex expression showing 11x + 4x = 105
c A LaTex expression showing 11x + 9x = 105
d A LaTex expression showing 11x - 9x = 105
e A LaTex expression showing 11x + 8x = 105
f A LaTex expression showing 10x + 4 = x
3
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 12m - d = 63\\d = 3m\\m = ?
a A LaTex expression showing 12m + 3m = 63
b A LaTex expression showing 10m + 3 = m
c A LaTex expression showing 12m - 9m = 63
d A LaTex expression showing 12m - 3m = 63
e A LaTex expression showing 12m + 9m = 63
f A LaTex expression showing 12m + 3 = 63
4
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 6r + d = 40\\d = 2r\\r = ?
a A LaTex expression showing 6r + 6r = 40
b A LaTex expression showing 6r - 7r = 40
c A LaTex expression showing 8r + 2 = r
d A LaTex expression showing 6r + 2 = 40
e A LaTex expression showing 6r + 7r = 40
f A LaTex expression showing 6r + 2r = 40
5
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 6z + b = 36\\b = 12z\\z = ?
a A LaTex expression showing 6z + 12 = 36
b A LaTex expression showing 6z - 4z = 36
c A LaTex expression showing 6z + 12z = 36
d A LaTex expression showing 6z + 3z = 36
e A LaTex expression showing 5z + 12 = z
f A LaTex expression showing 6z + 4z = 36
6
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 12z + r = 92\\r = 11z\\z = ?
a A LaTex expression showing 12z - 6z = 92
b A LaTex expression showing 12z + 11 = 92
c A LaTex expression showing 7z + 11 = z
d A LaTex expression showing 12z + 6z = 92
e A LaTex expression showing 12z + 11z = 92
f A LaTex expression showing 12z + 5z = 92
7
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 7d - n = 2\\n = 6d\\d = ?
a A LaTex expression showing 5d + 6 = d
b A LaTex expression showing 7d + 6 = 2
c A LaTex expression showing 7d - 6d = 2
d A LaTex expression showing 7d + 6d = 2
e A LaTex expression showing 7d + 4d = 2
f A LaTex expression showing 7d - 4d = 2