SOLVING LINEAR EQUATIONS WITH UNKNOWN COEFFIENTS WORKSHEET

Problem 1 :

5x + 16y = 36 

cx + dy = 9

The system of equations above, where c and d are constants, has infinity many solutions. What is the value of cd ?

Solution

Problem 2 :

0.3x - 0.7y = 1

kx - 2.8y = 3

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

Solution

Problem 3 :

x + ay = 5

2x + 6y = b

In the system of 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 = 12

c)  a = 3, b = -4        d)  a = 10, b = 3

Solution

Problem 4 :

y = ax + b

y = -bx

The equation of two lines in the xy-plane are shown above, where a and b are constants. If the two lines intersect at (2, 8), what is the value of a ?

(a)  2   (b)  4   (c)  6   (d)  8

Solution

Problem 5 :

2x - 5y = a

bx + 10y = -8

If the system of equations above, a and b are constants. If the system has infinitely many solutions. What is the value of a ?

(a)  -4    (b) 1/4    (c)  4    (d)  16 

Solution

Problem 6 :

(1/3) x - (1/6)y = 4

6x - ay = 8

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

(a)  1/3   (b) 1  (c)  3   (d)  6

Solution

Problem 7 :

mx - 6y = 10

2x - ny = 5

In he system of equations above, m and n are constants. If the system has infinitely many solutions, what is the value of m/n ?

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 :

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 6 :

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 7 :

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