SOLVING LINEAR EQATIONS IN ONE VARIABLE SPECIAL CASES WORKSHEET

Determine if each equation has one solution, many solutions, or no solution. If the equation has a solution, determine the solution to the equation.

1)  2x - x + 7 = x + 3 + 4               Solution

2)  -2(x + 1) = -2x + 5        Solution

3)  4x + 2x + 2 = 3x - 7        Solution

4) 2(x + 2) + 3x = 2(x + 1) + 1      Solution

5)  4(x - 1) = 1/2(x - 8)      Solution

6)  1/2(2 - 4x) + 2x = 13      Solution

7)  3x - x + 4 = 4(2x - 1)      Solution

8)  4(2x + 1) = 5x + 3x + 9      Solution

9)  10 + x = 5(1/5x + 2)      Solution

10)  8(x + 2) = 2x + 16      Solution

11)  3 + 3/2x + 4 = 4x - 5/2x      Solution

Solving system linear 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

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

Problem 1 :

For what value of k the pair of equations

x + (k + 1) y = 5

(k + 1)x + 9y = 8k - 1

has infinitely many solutions.

Solution

Problem 2 :

Find the value of k for which the pair of equations

2x + 3y = 7

(k - 1)x + (k + 2)y = 3k

has infinitely many solutions.

Solution

Problem 3 :

For what value of k the pair of equations

kx + 2y = 5

3x - 4y = 10

has no solution.

Solution

Problem 4 :

For what value of k the pair of equations

3x + y = 1

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

has no solution.

Solution

Problem 5 :

Show that the system of equations

3x + 4y = 8

6x + 8y = 10

is inconsistent.

Solution

Problem 6 :

For what value of k for which the pair of equations.

2x + 5y = 0

kx + 10y = 0

has a non zero solution.

Solution