This math topic delves into the practice of solving linear systems of equations using the method of substitution. Specifically, it involves substituting one equation into another to eliminate one of the variables and form a single, solvable algebraic equation. Students learn and apply algebraic techniques to find the value of unknown variables that satisfy both equations in the system, enhancing their problem-solving and algebraic manipulation skills in the context of introductory 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 8x + 8z = 96\\z = 5x\\x = ?
a A LaTex expression showing 8x + 40x = 96
b A LaTex expression showing 8x - 4x = 96
c A LaTex expression showing 8x + 4x = 96
d A LaTex expression showing 5x + 5 = x
e A LaTex expression showing 8x + 5 = 96
f A LaTex expression showing 8x - 5x = 96
2
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 2n + 12c = 100\\c = 4n\\n = ?
a A LaTex expression showing 2n + 48n = 100
b A LaTex expression showing 2n + 4n = 100
c A LaTex expression showing 2n + 4 = 100
d A LaTex expression showing 2n - 5n = 100
e A LaTex expression showing 5n + 4 = n
f A LaTex expression showing 2n - 4n = 100
3
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 6y + 5c = 112\\c = 10y\\y = ?
a A LaTex expression showing 6y + 50y = 112
b A LaTex expression showing 6y + 10 = 112
c A LaTex expression showing 6y - 4y = 112
d A LaTex expression showing 5y + 10 = y
e A LaTex expression showing 6y + 4y = 112
f A LaTex expression showing 6y - 5y = 112
4
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 7d + 3n = 144\\n = 3d\\d = ?
a A LaTex expression showing 7d + 11d = 144
b A LaTex expression showing 12d + 3 = d
c A LaTex expression showing 7d + 9d = 144
d A LaTex expression showing 7d - 11d = 144
e A LaTex expression showing 7d - 12d = 144
f A LaTex expression showing 7d + 3 = 144
5
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 8c + 4n = 64\\n = 2c\\c = ?
a A LaTex expression showing 8c + 8c = 64
b A LaTex expression showing 8c + 2 = 64
c A LaTex expression showing 7c + 2 = c
d A LaTex expression showing 8c + 6c = 64
e A LaTex expression showing 8c - 7c = 64
f A LaTex expression showing 8c - 6c = 64
6
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 3y + 3p = 96\\p = 7y\\y = ?
a A LaTex expression showing 3y - 7y = 96
b A LaTex expression showing 3y + 7 = 96
c A LaTex expression showing 3y + 21y = 96
d A LaTex expression showing 3y + 6y = 96
e A LaTex expression showing 7y + 7 = y
f A LaTex expression showing 3y - 6y = 96
7
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 4x + 10r = 136\\r = 3x\\x = ?
a A LaTex expression showing 4x + 3 = 136
b A LaTex expression showing 4x + 30x = 136
c A LaTex expression showing 4x + 6x = 136
d A LaTex expression showing 4x - 6x = 136
e A LaTex expression showing 4x - 7x = 136
f A LaTex expression showing 7x + 3 = x
8
Substitute the second variable equation into the first equation to form a single solvable equation
A LaTex expression showing 3b + 2p = 49\\p = 2b\\b = ?
a A LaTex expression showing 3b + 4b = 49
b A LaTex expression showing 3b - 9b = 49
c A LaTex expression showing 3b + 2 = 49
d A LaTex expression showing 3b + 9b = 49
e A LaTex expression showing 3b - 10b = 49
f A LaTex expression showing 10b + 2 = b