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.

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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 3p + y = 90\\y = 7p\\p = ?
a A LaTex expression showing 3p - 11p = 90
b A LaTex expression showing 12p + 7 = p
c A LaTex expression showing 3p + 11p = 90
d A LaTex expression showing 3p + 10p = 90
e A LaTex expression showing 3p + 7 = 90
f A LaTex expression showing 3p + 7p = 90
2
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 10y - z = 24\\z = 7y\\y = ?
a A LaTex expression showing 10y - 7y = 24
b A LaTex expression showing 10y - 10y = 24
c A LaTex expression showing 10y + 7y = 24
d A LaTex expression showing 10y + 10y = 24
e A LaTex expression showing 10y + 7 = 24
f A LaTex expression showing 11y + 7 = y
3
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 8p + y = 70\\y = 2p\\p = ?
a A LaTex expression showing 8p - 9p = 70
b A LaTex expression showing 8p + 2 = 70
c A LaTex expression showing 8p + 8p = 70
d A LaTex expression showing 8p + 9p = 70
e A LaTex expression showing 10p + 2 = p
f A LaTex expression showing 8p + 2p = 70
4
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 10m - c = 30\\c = 4m\\m = ?
a A LaTex expression showing 10m + 7m = 30
b A LaTex expression showing 10m + 4m = 30
c A LaTex expression showing 10m - 7m = 30
d A LaTex expression showing 10m - 4m = 30
e A LaTex expression showing 10m + 4 = 30
f A LaTex expression showing 8m + 4 = m
5
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 4b - r = 9\\r = 3b\\b = ?
a A LaTex expression showing 4b - 3b = 9
b A LaTex expression showing 12b + 3 = b
c A LaTex expression showing 4b + 3 = 9
d A LaTex expression showing 4b + 11b = 9
e A LaTex expression showing 4b - 11b = 9
f A LaTex expression showing 4b + 3b = 9
6
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 10r + m = 42\\m = 11r\\r = ?
a A LaTex expression showing 5r + 11 = r
b A LaTex expression showing 10r + 4r = 42
c A LaTex expression showing 10r + 3r = 42
d A LaTex expression showing 10r + 11r = 42
e A LaTex expression showing 10r + 11 = 42
f A LaTex expression showing 10r - 4r = 42
7
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 + 3z = 36
b A LaTex expression showing 6z + 12 = 36
c A LaTex expression showing 6z + 12z = 36
d A LaTex expression showing 5z + 12 = z
e A LaTex expression showing 6z - 4z = 36
f A LaTex expression showing 6z + 4z = 36
8
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 5m + x = 63\\x = 4m\\m = ?
a A LaTex expression showing 10m + 4 = m
b A LaTex expression showing 5m + 9m = 63
c A LaTex expression showing 5m - 9m = 63
d A LaTex expression showing 5m + 4 = 63
e A LaTex expression showing 5m + 4m = 63
f A LaTex expression showing 5m + 8m = 63