SOLVING SYSTEM OF SIMULTANEOUS LINEAR EQUATIONS

Solve these simultaneous equations.

Problem 1 :

4x + y = 8

x + y = 5

Solution:

4x + y = 8 ---> (1)

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

Subtracting equation (1) & (2),

3x = 3

x = 1

By applying x = 1 in equation (1)

4(1) + y = 8

4 + y = 8

y = 4

So, the solution is x = 1 and y = 4.

Problem 2 :

3x + y = 7

3x + 2y = 5

Solution:

3x + y = 7 ---> (1)

3x + 2y = 5 ---> (2)

Subtracting equation (1) & (2),

-y = 2

y = -2

By applying y = -2 in equation (1)

3x - 2 = 7

3x = 9

x = 3

So, the solution is x = 3 and y = -2.

Problem 3 :

4x + y = 3

3x - y = 11

Solution:

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

3x - y = 11 ---> (2)

Adding equation (1) & (2)

7x = 14

x = 2

By applying x = 2 in equation (1)

4(2) + y = 3

8 + y = 3

y = -5

So, the solution is x = 2 and y = -5.

Problem 4 :

3x + 4y = 7

x - 4y = 5

Solution:

3x + 4y = 7 ---> (1)

x - 4y = 5 ---> (2)

Adding equation (1) & (2)

4x = 12

x = 3

By applying x = 3 in equation (1)

3(3) + 4y = 7

9 + 4y = 7

4y = -2

y = -1/2

So, the solution is x = 3 and y = -1/2.

Problem 5 :

2x + y = 11

x - 3y = 9

Solution:

2x + y = 11 ---> (1)

x - 3y = 9 ---> (2)

Multiply the equation (1) by 3, we get

6x + 3y = 33 ---> (3)

Adding equation (2) & (3)

7x = 42

x = 6

By applying x = 6 in equation (1)

2(6) + y = 11

12 + y = 11

y = -1

So, the solution is x = 6 and y = -1.

Problem 6 :

2x + 3y = 11

3x + 2y = 4

Solution:

2x + 3y = 11 ---> (1)

3x + 2y = 4 ---> (2)

Multiply the equation (1) by 3, we get

6x + 9y = 33 ---> (3)

Multiply the equation (2) by 2, we get

6x + 4y = 8 ---> (4)

Subtracting equation (3) & (4)

5y = 25

y = 5

By applying y = 5 in equation (1)

2x + 3(5) = 11

2x + 15 = 11

2x = -4

x = -2

So, the solution is x = -2 and y = 5.

Problem 7 :

4x + y = 25

x - 3y = 16

Solution:

4x + y = 25 ---> (1)

x - 3y = 16 ---> (2)

Multiply the equation (1) by 3, we get

12x + 3y = 75 ---> (3)

Adding equation (2) & (3)

13x = 91

x = 7

By applying x = 7 in equation (1)

4(7) + y = 25

28 + y = 25

y = -3

So, the solution is x = 7 and y = -3.