This math topic involves solving systems of linear equations using the method of addition or subtraction to eliminate variables and find their values. The problems presented require manipulating multiples of one equation and adding or subtracting from another to isolate and solve for variables such as \(x\), \(d\), \(b\), \(y\), and \(c\). Each question offers multiple choice answers, enhancing problem-solving and critical thinking skills within the introductory unit of Algebra Systems of Equations.

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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 8d + 12r = 168\\3d + 2r = 43\\d = ?
a A LaTex expression showing d = 9
b A LaTex expression showing d = -90
c A LaTex expression showing d = 8
d A LaTex expression showing d = 43
e A LaTex expression showing d = -10
f A LaTex expression showing d = 12
2
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 7x + 6b = 40\\3x + 2b = 16\\x = ?
a A LaTex expression showing x = -2
b A LaTex expression showing x = 7
c A LaTex expression showing x = 3
d A LaTex expression showing x = 4
e A LaTex expression showing x = -8
f A LaTex expression showing x = 16
3
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 2y + 12c = 90\\6y + 6c = 60\\y = ?
a A LaTex expression showing y = -10
b A LaTex expression showing y = 60
c A LaTex expression showing y = 2
d A LaTex expression showing y = 6
e A LaTex expression showing y = -30
f A LaTex expression showing y = 3
4
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 4x + 12d = 68\\5x + 3d = 25\\x = ?
a A LaTex expression showing x = 2
b A LaTex expression showing x = 5
c A LaTex expression showing x = -16
d A LaTex expression showing x = 25
e A LaTex expression showing x = 1
f A LaTex expression showing x = -32
5
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 3c + 4b = 44\\8c + 2b = 74\\c = ?
a A LaTex expression showing c = 11
b A LaTex expression showing c = 8
c A LaTex expression showing c = 7
d A LaTex expression showing c = -104
e A LaTex expression showing c = 74
f A LaTex expression showing c = -13
6
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 7d + 10z = 85\\3d + 5z = 40\\d = ?
a A LaTex expression showing d = 8
b A LaTex expression showing d = 4
c A LaTex expression showing d = 5
d A LaTex expression showing d = 1
e A LaTex expression showing d = 40
7
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 10x + 9p = 85\\6x + 3p = 39\\x = ?
a A LaTex expression showing x = 4
b A LaTex expression showing x = 39
c A LaTex expression showing x = 7
d A LaTex expression showing x = -8
e A LaTex expression showing x = 3
f A LaTex expression showing x = -32
8
Solve for the variable by adding or subtracting multiples of the second equation to the first
A LaTex expression showing 9n + 6c = 66\\7n + 2c = 46\\n = ?
a A LaTex expression showing n = 6
b A LaTex expression showing n = -72
c A LaTex expression showing n = 9
d A LaTex expression showing n = 5
e A LaTex expression showing n = 46
f A LaTex expression showing n = -12