This math topic focuses on solving systems of linear equations using variable substitution. Specifically, it involves substituting one variable from one equation into another to form a single equation that can be solved. The problems aim to develop and test the mastery of basic algebraic manipulation related to combining equations and isolating variables. Each question presents equations with variables to be substituted and includes multiple-choice answers, encouraging skills in solving for the unknown and verifying solutions. This subject area is targeted at students who are beginning their studies in algebra and systems of equations.

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Linear Equation Systems - Simple Variable Substitution To Equation Worksheet

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Linear Equation Systems - Simple Variable Substitution To Equation
1
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing m = 3z + 7\\m = 2z + 13\\z = ?
a A LaTex expression showing 3z - 7 = 9z + 13
b A LaTex expression showing 3z + 7 = 2z + 13
c A LaTex expression showing 7z + 2 = 13
d A LaTex expression showing 8z - 7 = 2z + 13
e A LaTex expression showing 3z - 13 = 2z + 13
f A LaTex expression showing 8z + 7 = 2z + 13
2
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing b = 6x - 4\\b = 3x + 5\\x = ?
a A LaTex expression showing 6x - 4 = 6x + 5
b A LaTex expression showing 5x + 4 = 3x + 5
c A LaTex expression showing 4x + 3 = 5
d A LaTex expression showing 5x - 4 = 3x + 5
e A LaTex expression showing 6x - 4 = 3x + 5
f A LaTex expression showing 6x - 5 = 3x + 5
3
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing p = 10y - 5\\p = 6y + 11\\y = ?
a A LaTex expression showing 10y - 5 = 6y + 11
b A LaTex expression showing 10y - 11 = 6y + 11
c A LaTex expression showing 5y + 6 = 11
d A LaTex expression showing 10y - 5 = 7y + 11
e A LaTex expression showing 6y - 5 = 6y + 11
f A LaTex expression showing 6y + 5 = 6y + 11
4
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing p = 9n + 8\\p = 8n + 15\\n = ?
a A LaTex expression showing 9n + 8 = 8n + 15
b A LaTex expression showing 8n + 8 = 15
c A LaTex expression showing 9n - 8 = 10n + 15
d A LaTex expression showing 9n - 15 = 8n + 15
e A LaTex expression showing 9n - 8 = 8n + 15
f A LaTex expression showing 9n + 8 = 10n + 15
5
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing x = 8b - 5\\x = 6b + 3\\b = ?
a A LaTex expression showing 6b - 5 = 6b + 3
b A LaTex expression showing 6b + 5 = 6b + 3
c A LaTex expression showing 5b + 6 = 3
d A LaTex expression showing 8b - 5 = 6b + 3
e A LaTex expression showing 8b - 3 = 6b + 3
f A LaTex expression showing 8b - 5 = 7b + 3
6
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing x = 11m + 6\\x = 2m + 33\\m = ?
a A LaTex expression showing 11m - 33 = 2m + 33
b A LaTex expression showing 6m + 2 = 33
c A LaTex expression showing 11m + 6 = 2m + 33
d A LaTex expression showing 11m - 6 = 6m + 33
e A LaTex expression showing 5m - 6 = 2m + 33
f A LaTex expression showing 5m + 6 = 2m + 33
7
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing c = 8m + 12\\c = 4m + 36\\m = ?
a A LaTex expression showing 8m - 12 = 4m + 36
b A LaTex expression showing 12m + 4 = 36
c A LaTex expression showing 8m + 12 = 4m + 36
d A LaTex expression showing 8m + 12 = 9m + 36
e A LaTex expression showing 8m - 36 = 4m + 36
f A LaTex expression showing 8m - 12 = 9m + 36
8
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing b = 5z + 10\\b = 3z + 22\\z = ?
a A LaTex expression showing 5z - 10 = 9z + 22
b A LaTex expression showing 5z - 22 = 3z + 22
c A LaTex expression showing 8z + 10 = 3z + 22
d A LaTex expression showing 10z + 3 = 22
e A LaTex expression showing 8z - 10 = 3z + 22
f A LaTex expression showing 5z + 10 = 3z + 22