This math topic involves solving systems of linear equations through substitution. Each problem provides a pair of linear equations with variables, and the task is to substitute one equation into the other to form a single solvable equation. The goal is to simplify the equations to find the value of one variable. Multiple choice answers are provided for selecting the correctly simplified equation. This is an introductory exercise to the broader subject of algebraic systems of equations, aimed at developing skills in equation manipulation and substitution.

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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 7x + y = 51\\y = 2x + 6\\x = ?
a A LaTex expression showing 6x + 2x + 3 = 51
b A LaTex expression showing 7x + 2x + 4 = 6
c A LaTex expression showing 7x + 6x - 7 = 51
d A LaTex expression showing 7x + 2x + 6 = 51
e A LaTex expression showing 7x + 6x + 7 = 51
f A LaTex expression showing 6x - 2x - 3 = 51
2
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 5d + r = 72\\r = 3d + 8\\d = ?
a A LaTex expression showing 10d + 3d + 8 = 72
b A LaTex expression showing 9d - 3d - 6 = 72
c A LaTex expression showing 9d + 3d + 6 = 72
d A LaTex expression showing 5d + 3d + 7 = 9
e A LaTex expression showing 5d + 3d + 8 = 72
f A LaTex expression showing 5d + 9d + 10 = 72
3
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 7r + b = 97\\b = 10r + 12\\r = ?
a A LaTex expression showing 7r + 10r + 4 = 6
b A LaTex expression showing 6r - 10r - 3 = 97
c A LaTex expression showing 7r + 6r - 7 = 97
d A LaTex expression showing 6r + 10r + 3 = 97
e A LaTex expression showing 7r + 10r + 12 = 97
f A LaTex expression showing 7r + 6r + 7 = 97
4
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 11p - d = 36\\d = 3p + 4\\p = ?
a A LaTex expression showing 6p - 3p - 3 = 36
b A LaTex expression showing 11p - 6p + 7 = 36
c A LaTex expression showing 11p - 3p - 4 = 6
d A LaTex expression showing 11p - 3p - 4 = 36
e A LaTex expression showing 7p + 3p - 4 = 36
f A LaTex expression showing 6p - 3p + 3 = 36
5
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 9c + z = 86\\z = 5c + 2\\c = ?
a A LaTex expression showing 9c + 7c + 8 = 86
b A LaTex expression showing 7c - 5c - 4 = 86
c A LaTex expression showing 7c + 5c + 4 = 86
d A LaTex expression showing 9c + 5c + 2 = 86
e A LaTex expression showing 9c + 5c + 5 = 7
f A LaTex expression showing 8c + 5c + 2 = 86
6
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 10y - z = 7\\z = 5y + 3\\y = ?
a A LaTex expression showing 10y - 3y + 4 = 7
b A LaTex expression showing 3y - 5y - 0 = 7
c A LaTex expression showing 3y - 5y + 0 = 7
d A LaTex expression showing 10y - 5y - 1 = 3
e A LaTex expression showing 4y + 5y - 3 = 7
f A LaTex expression showing 10y - 5y - 3 = 7
7
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 11z + p = 58\\p = 5z + 10\\z = ?
a A LaTex expression showing 4z - 5z - 1 = 58
b A LaTex expression showing 11z + 4z + 5 = 58
c A LaTex expression showing 5z + 5z + 10 = 58
d A LaTex expression showing 4z + 5z + 1 = 58
e A LaTex expression showing 11z + 5z + 10 = 58
f A LaTex expression showing 11z + 5z + 2 = 4
8
Substitute the second equation into the first equation to form a single solvable equation
A LaTex expression showing 12c + d = 108\\d = 3c + 3\\c = ?
a A LaTex expression showing 8c - 3c - 5 = 108
b A LaTex expression showing 12c + 3c + 3 = 108
c A LaTex expression showing 9c + 3c + 3 = 108
d A LaTex expression showing 12c + 8c + 9 = 108
e A LaTex expression showing 8c + 3c + 5 = 108
f A LaTex expression showing 12c + 3c + 6 = 8