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Solving Linear Systems (using Linear Combinations) Worksheet

Solving Linear Systems (using Linear Combinations) Worksheet
  • Page 1
 1.  
Solve the linear system.
4x + 5y = 45
7x - 5y = 10
a.
(6, 5)
b.
(4, 5)
c.
(5, 5)
d.
(4, 4)


Solution:

4x + 5y = 45
[Equation 1.]

7x -  5y = 10
____________
[Equation 2.]

11x       =  55
[Add the equations.]

        x = 5
[Solve for x.]

4(5) + 5y = 45
[Substitute x = 5 in equation 1.]

20 + 5y = 45
[Multiply.]

5y = 25
[Subtract 20 from each side.]

y = 5
[Solve for y.]

The solution for the linear system is (5, 5).


Correct answer : (3)
 2.  
Solve the linear system.
-x + y = -20
17x - y = 68
a.
(17, 3)
b.
(3, -17)
c.
(17, -17)
d.
None of the above


Solution:

-x + y = -20
[Equation 1.]

17x - y = 68
___________
[Equation 2.]

16x       = 48
[Add the equations.]

     x = 3
[Solve for x.]

-3 + y = -20
[Substitute x = 3 in Equation 1.]

y = -17
[Solve for y.]

So, the solution for the linear system is (3, -17).


Correct answer : (2)
 3.  
Which of the following ordered pairs satisfies the linear system?
3x - 4y = 4
5x + 4y = 28
a.
(5, 1)
b.
(4, 2)
c.
(4, 3)
d.
(3, 3)


Solution:

3x - 4y = 4
[Equation 1.]

5x + 4y = 28
______________
[Equation 2.]

8x       = 32
[Add the equations.]

x = 4
[Solve for x.]

3(4) - 4y = 4
[Substitute 4 for x in equation 1.]

y = 2
[Solve for y.]

The solution for the linear system is (4, 2).


Correct answer : (2)
 4.  
Solve the linear system.
-5x - y = -15
-3x + y = -1
a.
(1, 5)
b.
(2, 5)
c.
(2, 6)
d.
None of the above


Solution:

-5x - y = -15
[Equation 1.]

-3x + y = -1
______________
[Equation 2.]

-8x        = -16
[Add the equations.]

        x = 2
[Solve for x.]

-5(2) - y = -15
[Substitute x = 2 in Equation 1.]

y = 5
[Solve for y.]

The solution for the linear system is (2, 5).


Correct answer : (2)
 5.  
Solve the linear system.
x - 3y = -13
-x + 7y = 37
a.
(5, 6)
b.
(6, 5)
c.
(5, 9)
d.
None of the above


Solution:

x - 3y = -13
[Equation 1.]

-x + 7y = 37
____________
[Equation 2.]

      4y = 24
[Add the equations.]

       y = 6
[Solve for y.]

x - 3(6) = -13
[Substitute y = 6 in Equation 1.]

x = 5
[Solve for x.]

So, the solution for the linear system is (5, 6).


Correct answer : (1)
 6.  
Solve the linear system.
3x + y = 22
-4x - 2y = -26
a.
(-9, 5)
b.
(9, 5)
c.
(9, -5)
d.
(-9, -5)


Solution:

Eliminate x from both the equations by making the coefficient of x in one equation opposite to the other.

  12x + 4y = 88
[Multiply Equation 1 by 4.]

-12x - 6y = -78
_______________
[Multiply Equation 2 by 3.]

          -2y = 10
[Add the equations.]

        y = -5
[Solve for y.]

3x + (-5) = 22
[Substitute y = -5 in Equation 1.]

x = 9
[Solve for x.]

The solution for the linear system is (9, -5).


Correct answer : (3)
 7.  
Which of the following ordered pairs satisfies the given linear system?
x - 4y = -22
-3x - 5y = -36
a.
(-2, 6)
b.
(-2, 0)
c.
(2, 6)
d.
None of the above


Solution:

 3x - 12y = -66
[Multiply Equation 1 by 3.]

-3x - 5y = -36
______________
[Equation 2.]

       -17y = -102
[Add the Equations.]

        y = 6
[Solve for y.]

x - 4(6) = -22
[Substitute y = 6 in Equation 1.]

x - 24 = -22
[Multiply.]

x = -22 + 24
[Add 24 to each side.]

x = 2
[Solve for x.]

So, the solution for the linear system is (2, 6).


Correct answer : (3)
 8.  
Which of the following ordered pairs satisfies the given linear system?
-x + y = -2 --- Equation 1
-3x - 3y = -30 --- Equation 2
a.
(6, -4)
b.
(6, 4)
c.
(-6, 4)
d.
None of the above


Solution:

-x - y = -10
[Divide Equation 2 by 3.]

-x + y = -2
[Equation 1.]

-x - y = -10
_____________
[Revised Equation 2.]

-2x      = -12
[Add Equation 1 and revised Equation 2.]

x = 6
[Solve for x.]

-6 + y = -2
[Substitute 6 for x in revised Equation 2.]

y = 4
[Add 6 to each side.]

The solution for the linear system is (6, 4).


Correct answer : (2)
 9.  
Which of the following solutions satisfies the given linear system?
5x - y = -2
-4x + 5y = -11
a.
(-2, -3)
b.
(-3, 1)
c.
(-1, -3)
d.
None of the above


Solution:

25x - 5y = -10
[Multiply Equation 1 by 5.]

-4x + 5y = -11
______________
[Multiply Equation 2 by 1.]

21x         = -21
[Add the equations.]

         x = -1
[Solve for x.]

5(-1) - y = -2
[Substitute x = -1 in Equation 1.]

y = -3
[Solve for y.]

Solution for the linear system is (-1, -3).


Correct answer : (3)
 10.  
Which of the following ordered pairs satisfies the given linear system?
-5x + 4y = -4
4y = 4 + 3x
a.
(4, 4)
b.
(-4, 5)
c.
(3, 4)
d.
None of the above


Solution:

-5x + 4y = -4
[Equation 1.]

3x - 4y = -4
____________
[Rearrange Equation 2 and multiply with -1.]

-2x       = -8
[Add the equations.]

x = 4
[Solve for x.]

-5(4) + 4y = -4
[Substitute 4 for x in Equation 1.]

-20 + 4y = -4
[Multiply.]

4y = 16
[Add 20 on each side.]

y = 4
[Solve for y.]

Solution for the linear system is (4, 4).


Correct answer : (1)

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