SOLVING SYSTEMS OF EQUATIONS SPECIAL CASES WORKSHEET

Problem 1 :

For what value of c will the system of equations below have no solution ?

cx - 2y = 6

3x + 4y = 4

Solution

Problem 2 :

For what value of b will the system of equations below have infinitely many solution ?

-2x + y = 4

5x - by = -10

Solution

Problem 3 :

ax - y = 0

x - by = 1

In the system of equations above, a and b are constants and x and y are variables. If the system of equations above has no solution. What is the value of a ⋅ b ?

Solution

Problem 4 :

2x - ky = 14

5x - 2y = 5

In the system of equations above, k is constant and x and y are variables. For what values of k will the system of equations have no solution ?.        Solution

Without graphing, determine whether the system of linear equations has one solution, infinitely many solutions, or no solution. Explain your reasoning.

Problem 5 :

y = 5x - 9

y = 5x + 9

Solution

Problem 6 :

y = 6x + 2 

y = 3x + 1

Solution

Problem 7 :

y = 8x - 2

y - 8x = -2

Solution

Problem 1 :

x - 3y = 4

2(x - 1) - 6(y + 2) = -6

How many solutions (x, y) are there to the system of equations above ?

(a) Zero   (b) One   (c)  Two    (d)  More than two

Solution

Problem 2 :

ax + 4y = 14

5x + 7y = 8

In the system of equations above, a is a constant and x and y are variables. If the system has no solution, what is the value of a ?

(a)  20/7    (b)  -35/4     (c)  35/4     (d) - 20/7

Solution

Problem 3 :

ax + (1/2)y = 16

4x + 3y = 8

In the system of equations above, a is constant. If the system has no solution, what is the value of a ?

(a)  2/3     (b) 8      (c)  8     (d)  24

Solution

Problem 4 :

3x + ky = 8

x + 4y = -1

If (x, y) is a solution to the system of equations above and k is constant, what is y in terms of k ?

(a)  5/(k - 12)      (b)  5/(k - 12)      (c)  11/(k - 12)     (d) 9/(k-4)

Solution

Problem 5 :

x/(y + 2) = 2

3(y - 5) - x = -16

If (x, y) is the solution to the system of equations above, what is the value of x ?              Solution

Problem 6 :

-2x - y = -9

5x - 2y = 18

Which of the following ordered pairs (x, y) fulfills the system of equations above ?

(a) (-4, 1)      (b)  (3, 3)     (c) (2, 5)   (d)  (4, 1)

Solution

Problem 7 :

-3x + 2y = 5

-9x + 6y = 18

The system of equations above has how many solutions (x, y)

(a) Zero      (b)  Two     (c) One   (d) More than two

Solution

Problem 1 :

Which ordered pair (x, y) satisfies the system of equations below ?

5x+ y = 9

10x - 7y = -18

(a)  (-2, 19)    (b)  (1, 4)     (c) (3, -6)      (d)  (5, -1)

Solution

Problem 2 :

2x - 3y = -1

-x + y = -1

According to the systems of equations above, what is the value of x ?

Solution

Problem 3 :

-4x - 15y = -17

-x + 5y = -13

If (x, y) is the solution to the system of equations above, what is the value of x ?

Solution

Problem 4 :

0.3x - 0.7y = 1

kx - 2.8y  = 3

In the system of equations above, k is constant if the system has no solution, what is the value of k ?

Solution

Problem 5 :

-2x + 6y = 10

-3x + 9y = 18

How many solutions (x, y) are there to the system of the equations above. ?

(a)  Zero     (b)  one      (c) Two      (d)  More than two

Solution

Problem 6 :

3x - 2y = 6

9x - 6y = 2a

Solution

Problem 7 :

x + ay = 5

2x + 6y = b

In the system equations above a and b are constants. If the system has one solution, which of the following could be the values of a and b ?

(a)  a = 3, b = 10    (b)  a = 3, b = -4

(c)  a = 3, b = 12     (d) a = 10, b = 3

Solution