Solved Examples and Worksheet for Solving Systems of Equations by Elimination Method

Q1Which of the following ordered pairs satisfies the given linear system?
-5x + y = -12
-5x - y = 42
A. (-3, -27)
B. (-27, 3)
C. (-27, -3)
D. (3, -27)

Solutions
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Step: 1
-5x + y = -12
  [Equation 1.]
Step: 2
-5x - y = 42
_____________
  [Equation 2.]
Step: 3
-10x       = 30
  [Add the Equations 1 and 2.]
Step: 4
x = -3
  [Solve for x.]
Step: 5
-5(-3) + y = -12
  [Substitute -3 for x in Equation 1.]
Step: 6
y = -27
  [Solve for y.]
Step: 7
The solution for the linear system is (-3, -27).
Correct Answer is :   (-3, -27)
Q2Which of the following ordered pairs satisfies the given linear system?
4x - 5y = -2
-6x + 5y = 8

A. (-3, 2)
B. (3, -2)
C. (3, 2)
D. (-3, -2)

Solutions
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Step: 1
4x - 5y = -2
  [Equation 1.]
Step: 2
-6x + 5y = 8
____________
  [Equation 2.]
Step: 3
-2x      = 6
  [Add the equations.]
Step: 4
x = -3
  [Solve for x.]
Step: 5
4(-3) - 5y = -2
  [Substitute -3 for x in Equation 1.]
Step: 6
y = -2
  [Solve for y.]
Step: 7
The solution for the linear system is (-3, -2).
Correct Answer is :   (-3, -2)
Q3Which of the following ordered pairs satisfies the given linear system?
2x + 7y = 7
-2x + 7y = -21

A. (-7, -1)
B. (-7, 1)
C. (7, -1)
D. (7, 1)

Solutions
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Step: 1
2x + 7y = 7
  [Equation 1.]
Step: 2
-2x + 7y = -21
____________
  [Equation 2.]
Step: 3
      14y = -14
  [Add the equations.]
Step: 4
y = -1
  [Solve for y.]
Step: 5
2x + 7(-1) = 7
  [Substitute -1 for y in Equation 1.]
Step: 6
x = 7
  [Solve for x.]
Step: 7
The solution for the linear system is (7, -1).
Correct Answer is :   (7, -1)
Q4Solve the linear system.
6x +5y = 10 --- (1)
-5x + 6y = 12 --- (2)

A. (0, 2)
B. (1, 3)
C. (2, 0)
D. (1, 2)

Solutions
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Step: 1
 30x + 25y = 50
  [Multiply Equation 1 by 5.]
Step: 2
-30x + 36y = 72
________________
  [Multiply Equation 2 by 6.]
Step: 3
           61y = 122
  [Add the equations.]
Step: 4
        y = 2
  [Solve for y.]
Step: 5
6x + 5(2) = 10
  [Substitute y = 2 in Equation 1.]
Step: 6
6x + 10 = 10
  [Multiply.]
Step: 7
6x = 0
  [Subtract 10 from each side.]
Step: 8
x = 0
  [Solve for x.]
Step: 9
The solution for the linear system is (0, 2).
Correct Answer is :   (0, 2)
Q5Solve the linear system.
x + 2y = -4
-3x + 4y = -28
A. (4 , -4 )
B. (-4 , 4 )
C. (-4 , -4 )
D. (4 , 4 )

Solutions
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Step: 1
3x + 6y = -12
  [Multiply Equation 1 by 3.]
Step: 2
-3x + 4y = -28
_____________
  [Multiply Equation 2 by 1.]
Step: 3
        10y = -40
  [Add the equations.]
Step: 4
y = -4
  [Solve for y.]
Step: 5
x + 2(-4) = -4
  [Substitute -4 for y in Equation 1.]
Step: 6
x - 8 = -4
  [Multiply.]
Step: 7
x = 4
  [Add 8 to each side.]
Step: 8
The solution for the linear system is (4, -4).
Correct Answer is :   (4 , -4 )
Q6Solve the linear system.
x - 3y = 10 --- (1)
-1x + 4y = -15 --- (2)
A. (-5 , -5 )
B. (-5 , 5 )
C. (5 , 5 )
D. (5 , -5 )

Solutions
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Step: 1
 1x - 3y = 10
  [Multiply equation 1 by 1.]
Step: 2
-1x + 4y = -15
_______________
  [Multiply equation 2 by 1.]
Step: 3
        1y = -5
  [Add the equations.]
Step: 4
        y = -5
  [Solve for y.]
Step: 5
x - 3(-5) = 10
  [Substitute y = -5 in Equation 1.]
Step: 6
x + 15 = 10
  [Multiply.]
Step: 7
x = 10 - 15
  [Subtract 15 from each side.]
Step: 8
x = -5
  [Solve for x.]
Step: 9
The solution for the linear system is (-5, -5)
Correct Answer is :   (-5 , -5 )
Q7Solve the linear system.
x - 5y = - 4
- 4x + 5y = 16

A. (0, -4 )
B. (-4 , 0)
C. (0, 4 )
D. (4 , 0)

Solutions
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Step: 1
4x - 20y = -16
  [Multiply Equation 1 by 4.]
Step: 2
-4x + 5y = 16
_______________
  [Multiply Equation 2 by 1.]
Step: 3
       -15y = 0
  [Add the equations.]
Step: 4
y = 0
  [Solve for y.]
Step: 5
x - 5(0) = -4
  [Substitute 0 for y in Equation 1.]
Step: 6
x - 0 = -4
  [Multiply.]
Step: 7
x = -4
  [Solve for x.]
Step: 8
The solution for the linear system is (-4, 0).
Correct Answer is :   (-4 , 0)
Q8Solve the linear system.
3x - 4y = 7 --- (1)
-4x + 5y = -11 --- (2)
A. (9 , -5 )
B. (9 , 5 )
C. (-9 , -5 )
D. (-9 , 5 )

Solutions
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Step: 1
 12x - 16 y = 28
  [Multiply Equation 1 by 4.]
Step: 2
-12x + 15 y = -33
______________
  [Multiply Equation 2 by 3.]
Step: 3
            -1y = -5
  [Add the Equations.]
Step: 4
          y = 5
  [Solve for y.]
Step: 5
3x - 4(5) = 7
  [Substitute y = 5 in Equation 1.]
Step: 6
3x - 20 = 7
  [Multiply.]
Step: 7
3x = 27
  [Add 20 to each side.]
Step: 8
x = 9
  [Solve for x.]
Step: 9
The solution for the linear system is (9, 5).
Correct Answer is :   (9 , 5 )
Q9Solve the linear system.
x - 3y = 11
-3x - 5y = -5

A. (5, -2)
B. (5, 2)
C. (-2, 5)
D. (-5, -2)

Solutions
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Step: 1
3x - 9y = 33
  [Multiply Equation 1 by 3.]
Step: 2
-3x - 5y = -5
______________
  [Multiply Equation 2 by 1.]
Step: 3
       -14y = 28
  [Add the equations.]
Step: 4
y = -2
  [Solve for y.]
Step: 5
x - 3(-2) = 11
  [Substitute -2 for y in Equation 1.]
Step: 6
x + 6 = 11
  [Multiply y.]
Step: 7
x = 5
  [Solve for x.]
Step: 8
The solution for the linear system is (5, -2).
Correct Answer is :   (5, -2)
Q10Solve the linear system.
4x + y = -36 --- (1)
3x - 2y = 6 --- (2)
A. (6, -11)
B. (-6, -12)
C. (8, -10)
D. None of the above

Solutions
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Step: 1
8x + 2y = -72
  [Multiply Equation 1 by 2.]
Step: 2
 3x - 2y = 6
________________
  [Multiply Equation 2 by 1.]
Step: 3
 11x       = -66
  [Add the equations.]
Step: 4
         x = -6
  [Solve for x.]
Step: 5
4(-6) + y = -36
  [Substitute x = -6 in Equation 1.]
Step: 6
-24 + y = -36
  [Multiply.]
Step: 7
y = -12
  [Add 24 on each side.]
Step: 8
The solution for the linear system is (-6, -12).
Correct Answer is :   (-6, -12)
Q11Solve the linear system.
-4x - 3y = -21
10x + 9y = 57
A. (-3, 3)
B. (3, 3)
C. (3, -3)
D. (-3, -3)

Solutions
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Step: 1
-12x - 9y = -63
  [Multiply Equation 1 by 3.]
Step: 2
10x + 9y = 57
_____________
  [Multiply Equation 2 by 1.]
Step: 3
-2x         = -6
  [Add the equations.]
Step: 4
x = 3
  [Solve for x.]
Step: 5
-4(3) - 3y = -21
  [Substitute 3 for x in Equation 1.]
Step: 6
y = 3
  [Solve for y.]
Step: 7
The solution for the linear system is (3, 3).
Correct Answer is :   (3, 3)
Q12Solve the linear system.
4x + 3y = 22
3y = 14 - 2x

A. (-4, -2)
B. (4, -2)
C. (-4, 2)
D. (4, 2)

Solutions
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Step: 1
4x + 3y = 22
2x + 3y = 14
  [Arrange the equations with the like terms in columns.]
Step: 2
4x + 3y = 22
-2x - 3y = -14
_______________
  [Multiply equation 2 by -1 to get the coefficients of y to be opposites.]
Step: 3
2x       = 8
  [Add the equations.]
Step: 4
x = 4
  [Solve for x.]
Step: 5
4(4) + 3y = 22
  [Substitute 4 for x in Equation 1.]
Step: 6
16 + 3y = 22
  [Multiply.]
Step: 7
3y = 6
  [Subtract 16 from each side.]
Step: 8
y = 2
  [Solve for y.]
Step: 9
The solution for the linear system is (4, 2).
Correct Answer is :   (4, 2)
Q13Which of the following solutions satisfies the linear system?
3x + 4y = 5
-20y = -23 + 12x

A. (- 23, 34)
B. (23, 34)
C. (23, - 34)
D. (34, 23)

Solutions
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Step: 1
3x + 4y = 5
12x + 20y = 23
  [Arrange the equations with the like terms in columns.]
Step: 2
-15x - 20y = -25
  [Multiply equation 1 by -5.]
Step: 3
12x + 20y = 23
______________
  [Equation 2.]
Step: 4
-3x           = -2
  [Add.]
Step: 5
x = 23
  [Solve for x.]
Step: 6
3(23) + 4y = 5
  [Substitute 23 for x in Equation 1.]
Step: 7
2 + 4y = 5
  [Multiply.]
Step: 8
y = 34
  [Solve for y.]
Step: 9
The solution for the linear system is (23, 34).
Correct Answer is :   (23, 34)

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