The math topic being practiced here involves solving systems of linear equations using simple variable substitution. Each problem presents a system with one equation straightforwardly expressing one variable in terms of another. The task is to substitute this expression into another equation to isolate and solve for the remaining variable. The solutions are provided as multiple-choice answers, testing the student's ability to apply substitution correctly and simplify the equations to find the correct value of the variable in question. This is a fundamental skill in algebra, particularly useful in contexts where systems of equations frequently occur.

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Linear Equation Systems - Simple Variable Substitution Worksheet

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Linear Equation Systems - Simple Variable Substitution
1
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 5d + 3c = 68\\c = 4d\\d = ?
a A LaTex expression showing d = 3
b A LaTex expression showing d = 7
c A LaTex expression showing d = 4
d A LaTex expression showing d = 12
e A LaTex expression showing d = 2
f A LaTex expression showing d = 6
2
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 8m + 3n = 98\\n = 2m\\m = ?
a A LaTex expression showing m = 10
b A LaTex expression showing m = 7
c A LaTex expression showing m = 5
d A LaTex expression showing m = 6
e A LaTex expression showing m = 9
f A LaTex expression showing m = 6
3
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 9c + 4d = 148\\d = 7c\\c = ?
a A LaTex expression showing c = 6
b A LaTex expression showing c = 2
c A LaTex expression showing c = 4
d A LaTex expression showing c = 3
e A LaTex expression showing c = 7
f A LaTex expression showing c = 28
4
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 9n + 10c = 116\\c = 2n\\n = ?
a A LaTex expression showing n = 6
b A LaTex expression showing n = 4
c A LaTex expression showing n = 2
d A LaTex expression showing n = 7
e A LaTex expression showing n = 3
f A LaTex expression showing n = 20
5
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 2m + 8y = 52\\y = 3m\\m = ?
a A LaTex expression showing m = 4
b A LaTex expression showing m = 0
c A LaTex expression showing m = 2
d A LaTex expression showing m = 24
e A LaTex expression showing m = 5
f A LaTex expression showing m = 1
6
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 7m + 5c = 85\\c = 2m\\m = ?
a A LaTex expression showing m = 4
b A LaTex expression showing m = 8
c A LaTex expression showing m = 5
d A LaTex expression showing m = 10
e A LaTex expression showing m = 7
f A LaTex expression showing m = 3
7
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 12m + 2r = 110\\r = 5m\\m = ?
a A LaTex expression showing m = 10
b A LaTex expression showing m = 7
c A LaTex expression showing m = 5
d A LaTex expression showing m = 3
e A LaTex expression showing m = 4
f A LaTex expression showing m = 8
8
Solve for the variable by substituting the second equation into the first
A LaTex expression showing 10d + 10b = 120\\b = 5d\\d = ?
a A LaTex expression showing d = 5
b A LaTex expression showing d = 2
c A LaTex expression showing d = 0
d A LaTex expression showing d = 1
e A LaTex expression showing d = 50
f A LaTex expression showing d = 4