TYPES OF SOLUTIONS SYSTEM OF EQUATIONS WORKSHEET

Decide if the following systems of equations have a single solution, no solutions, or infinite solutions. If it has a solution, solve the system.

Problem 1 :

x + y = 1

x + y = 5

Solution

Problem 2 :

2x + 3y = 7

4x + 5y = 13

Solution

Problem 3 :

1/2x + 3y = 1

x + 6y = 2

Solution

Problem 4 :

x + (1/3)y = -10

3x + y = 30

Solution

Problem 5 :

2y = 6

3(x + y) = 12

Solution

Problem 6 :

x + y = 2

3x + 3y = 6

Solution

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

Problem 5 :

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 6 :

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 7 :

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 8 :

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 9 :

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 10 :

-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 11 :

-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