This math topic focuses on solving systems of linear equations using simple addition or subtraction techniques to simplify and solve for unknown variables. It covers problems where learners manipulate and combine equations to isolate and find the values of variables. Each problem consists of two equations with two variables, and the task is to solve for one of the variables by eliminating the other through addition or subtraction of the equations. Each question offers multiple choice answers, enhancing problem-solving and algebraic manipulation skills.

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Linear Equation Systems - Simple Addition Worksheet

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Linear Equation Systems - Simple Addition
1
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 12p + 10y = 78\\-6p + 2y = -18\\y = ?
a A LaTex expression showing y = 14
b A LaTex expression showing y = 2
c A LaTex expression showing y = 42
d A LaTex expression showing y = -18
e A LaTex expression showing y = 3
f A LaTex expression showing y = 6
2
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 2c + 4d = 28\\3c - 2d = 2\\c = ?
a A LaTex expression showing c = 3
b A LaTex expression showing c = 32
c A LaTex expression showing c = 7
d A LaTex expression showing c = 8
e A LaTex expression showing c = 2
f A LaTex expression showing c = 4
3
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 3p + 12z = 111\\4p - 4z = -12\\p = ?
a A LaTex expression showing p = 8
b A LaTex expression showing p = 5
c A LaTex expression showing p = 75
d A LaTex expression showing p = 4
e A LaTex expression showing p = 15
f A LaTex expression showing p = -12
4
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 4z + 8n = 28\\5z - 4n = 7\\z = ?
a A LaTex expression showing z = 6
b A LaTex expression showing z = 7
c A LaTex expression showing z = 2
d A LaTex expression showing z = 3
e A LaTex expression showing z = 14
f A LaTex expression showing z = 42
5
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 8c + 3n = 52\\-2c + 2n = -2\\n = ?
a A LaTex expression showing n = 11
b A LaTex expression showing n = 44
c A LaTex expression showing n = -2
d A LaTex expression showing n = 7
e A LaTex expression showing n = 4
f A LaTex expression showing n = 3
6
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 4n + 4p = 32\\-2n + 2p = -4\\p = ?
a A LaTex expression showing p = 6
b A LaTex expression showing p = -4
c A LaTex expression showing p = 8
d A LaTex expression showing p = 2
e A LaTex expression showing p = 24
f A LaTex expression showing p = 3
7
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 10x + 10y = 140\\2x - 5y = -7\\x = ?
a A LaTex expression showing x = -7
b A LaTex expression showing x = 8
c A LaTex expression showing x = 12
d A LaTex expression showing x = 126
e A LaTex expression showing x = 9
f A LaTex expression showing x = 14
8
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 2r + 10c = 90\\5r - 5c = -15\\r = ?
a A LaTex expression showing r = 5
b A LaTex expression showing r = 60
c A LaTex expression showing r = 12
d A LaTex expression showing r = -15
e A LaTex expression showing r = 4
f A LaTex expression showing r = 8