This math topic focuses on solving linear systems by simple equation substitution. The problems involve substituting one equation into another to solve for variables in algebraic equations. Students are tasked with solving systems, providing practice in manipulating equations to isolate variables and substituting correctly to find solutions. Multiple-choice answers are provided for each problem, requiring students to select the correct value of the variable from several options. This is a fundamental exercise for building skills in algebra and understanding systems of linear equations.

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Linear Equation Systems - Simple Equation Substitution Worksheet

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Linear Equation Systems - Simple Equation Substitution
1
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 3m + 5p = 79\\p = 7m - 7\\m = ?
a A LaTex expression showing m = 3
b A LaTex expression showing m = 6
c A LaTex expression showing m = 35
d A LaTex expression showing m = 2
e A LaTex expression showing m = 1
f A LaTex expression showing m = 35
2
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 12z + 2b = 150\\b = 3z + 12\\z = ?
a A LaTex expression showing z = 24
b A LaTex expression showing z = 7
c A LaTex expression showing z = 5
d A LaTex expression showing z = 6
e A LaTex expression showing z = 10
f A LaTex expression showing z = 6
3
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 7y + 4b = 53\\b = 5y - 7\\y = ?
a A LaTex expression showing y = 3
b A LaTex expression showing y = 6
c A LaTex expression showing y = 2
d A LaTex expression showing y = 28
e A LaTex expression showing y = 20
f A LaTex expression showing y = 1
4
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 4m + 3b = 5\\b = 5m - 11\\m = ?
a A LaTex expression showing m = 2
b A LaTex expression showing m = 15
c A LaTex expression showing m = 5
d A LaTex expression showing m = 1
e A LaTex expression showing m = 0
f A LaTex expression showing m = 33
5
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 3r + 6m = 93\\m = 4r + 2\\r = ?
a A LaTex expression showing r = 12
b A LaTex expression showing r = 1
c A LaTex expression showing r = 6
d A LaTex expression showing r = 2
e A LaTex expression showing r = 24
f A LaTex expression showing r = 3
6
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 5d + 7z = -25\\z = 2d - 9\\d = ?
a A LaTex expression showing d = 14
b A LaTex expression showing d = 63
c A LaTex expression showing d = 2
d A LaTex expression showing d = 5
e A LaTex expression showing d = 0
f A LaTex expression showing d = 1
7
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 5z + 5d = 95\\d = 11z - 5\\z = ?
a A LaTex expression showing z = 2
b A LaTex expression showing z = 55
c A LaTex expression showing z = 0
d A LaTex expression showing z = 5
e A LaTex expression showing z = 1
f A LaTex expression showing z = 25
8
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 5p + 6c = 148\\c = 10p + 3\\p = ?
a A LaTex expression showing p = 60
b A LaTex expression showing p = 2
c A LaTex expression showing p = 0
d A LaTex expression showing p = 1
e A LaTex expression showing p = 18
f A LaTex expression showing p = 5