SOLVING WITH UNKNOWNS IN MATRIX

Solve each equation.

Problem 1 :

Solution:

By comparing corresponding terms,

(x, y, z) = (2.5, 1, 3)

Problem 2 :

Solution:

By comparing corresponding terms

(x, y) = (3, -1/3)

Problem 3 :

Solution:

By comparing corresponding terms,

(x, y) = (5, 3)

Problem 4 :

Solution:

By comparing corresponding terms

(x, y, z) = (3, -5, 6)

Problem 5 :

Solution:

x + 3y = -13 ---> (1)

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

(1) × 3 ==> 3x + 9y = -39 ---> (3)

    (2) ==> 3x + y = 1

From (3) - (2)

8y = -40

y = -5

By applying y = -5 in (2),

3x - 5 = 1

3x = 6

x = 2

(x, y) = (2, -5)

Problem 6 :

Solution:

2x + y = 5 ---> (1)

x - 3y = 13 ---> (2)

(1) × 3 ==> 6x + 3y = 15 ---> (3)

(2) ==> x - 3y = 13

Add (2) & (3),

7x = 28

x = 28/7

x = 4

By applying x = 4 in (2),

4 - 3y = 13

-3y = 9

y = -3

(x, y) = (4, -3)

Problem 7 :

Solution:

2x = y 

2x - y = 0 ---> (1)

2x + 3y = 12 ---> (2)

From (1) - (2),

-4y = -12

y = 3

By applying y = 3 in (1),

2x - 3 = 0

2x = 3

x = 3/2

x = 1.5

(x, y) = (1.5, 3)

Problem 8 :

Solution:

4x = 11 + 3y

4x - 3y = 11 ---> (1)

y - 1 = x

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

(1) ==> 4x - 3y = 11

(2) × 4 ==> -4x + 4y = 4

(1) + (2),

y = 15

By applying y = 15 in (2)

-x + 15 = 1

-x = -14

x = 14

(x, y) = (14, 15)

Problem 9 :

Solution:

x + y = 5 ---> (1)

y - 4 = 3

y = 7

By applying y = 7 in (1)

7 + y = 5

y = -2

(x, y) = (-2, 7)

Problem 10 :

Solution:

3x + y = 9z

3(5) + 3 = 9z

15 + 3 = 9z

18 = 9z

z = 2

(x, y, z) = (5, 3, 2)

Solve each equation.

Problem 11 :

Solution:

By comparing corresponding terms, 

(x, y) = (5, 6)

Problem 12 :

Solution:

By comparing corresponding matrix,

x + 2y = 9 ---> (1)

4x + 1 = 13

4x = 12

x = 3

By applying x = 3 in (1)

3 + 2y = 9

3 + 2y = 9

2y = 6

y = 3

(x, y) = (3, 3)