This math topic focuses on solving systems of linear equations by substitution. It involves substituting one equation into another to form a single equation that can be solved for one variable. The problems provided require substituting a given expression into another equation and simplifying to solve for the unknown variable. This includes determining the correct simplified form from multiple answer choices. These exercises practice algebraic manipulation skills and help in understanding how to isolate variables to find specific solutions in linear equation systems.

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Linear Equation Systems - Simple Equation Substitution To Equation Worksheet

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Linear Equation Systems - Simple Equation Substitution To Equation
1
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 2z + 7m = 117\\m = 3z - 3\\z = ?
a A LaTex expression showing 2z + 21z - 21 = 117
b A LaTex expression showing 2z - 3z + 5 = 21
c A LaTex expression showing 21z + 3z - 4 = 117
d A LaTex expression showing 21z + 3z + 3 = 117
e A LaTex expression showing 21z - 3z - 4 = 117
f A LaTex expression showing 21z - 3z + 3 = 117
2
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 4p + 5d = 92\\d = 6p - 2\\p = ?
a A LaTex expression showing 10p + 6p + 2 = 92
b A LaTex expression showing 10p - 6p + 2 = 92
c A LaTex expression showing 30p + 6p - 1 = 92
d A LaTex expression showing 30p - 6p - 1 = 92
e A LaTex expression showing 4p - 6p + 2 = 30
f A LaTex expression showing 4p + 30p - 10 = 92
3
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 6d + 10y = 12\\y = 2d - 4\\d = ?
a A LaTex expression showing 40d - 2d + 4 = 12
b A LaTex expression showing 6d + 20d - 40 = 12
c A LaTex expression showing 6d - 2d + 1 = 20
d A LaTex expression showing 20d - 2d - 0 = 12
e A LaTex expression showing 20d + 2d - 0 = 12
f A LaTex expression showing 40d + 2d + 4 = 12
4
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 4n + 4z = 112\\z = 4n - 7\\n = ?
a A LaTex expression showing 16n - 4n - 5 = 112
b A LaTex expression showing 16n + 4n - 5 = 112
c A LaTex expression showing 28n + 4n + 7 = 112
d A LaTex expression showing 4n - 4n + 6 = 16
e A LaTex expression showing 4n + 16n - 28 = 112
f A LaTex expression showing 28n - 4n + 7 = 112
5
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 12b + 4x = 116\\x = 6b - 7\\b = ?
a A LaTex expression showing 12b + 24b - 28 = 116
b A LaTex expression showing 24b + 6b - 2 = 116
c A LaTex expression showing 28b - 6b + 7 = 116
d A LaTex expression showing 24b - 6b - 2 = 116
e A LaTex expression showing 12b - 6b + 3 = 24
f A LaTex expression showing 28b + 6b + 7 = 116
6
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 12d + 2b = 144\\b = 6d - 12\\d = ?
a A LaTex expression showing 12d - 6d - 5 = 144
b A LaTex expression showing 24d + 6d + 12 = 144
c A LaTex expression showing 24d - 6d + 12 = 144
d A LaTex expression showing 12d + 6d - 5 = 144
e A LaTex expression showing 12d + 12d - 24 = 144
f A LaTex expression showing 12d - 6d + 6 = 12
7
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 6m + 5p = 108\\p = 5m + 3\\m = ?
a A LaTex expression showing 6m + 5m + 2 = 25
b A LaTex expression showing 15m + 5m + 3 = 108
c A LaTex expression showing 6m + 25m - 15 = 108
d A LaTex expression showing 25m + 5m + 1 = 108
e A LaTex expression showing 6m + 25m + 15 = 108
f A LaTex expression showing 25m - 5m - 1 = 108
8
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 11p + 5c = 134\\c = 2p + 10\\p = ?
a A LaTex expression showing 10p - 2p - 2 = 134
b A LaTex expression showing 10p + 2p + 2 = 134
c A LaTex expression showing 11p + 10p + 50 = 134
d A LaTex expression showing 11p + 2p + 3 = 10
e A LaTex expression showing 11p + 10p - 50 = 134
f A LaTex expression showing 50p + 2p + 10 = 134