SOLVE THE SYSTEM OF LINEAR EQUATIONS BY ELIMINATION

Problem 1 :

3x + y = 7

-2x - y = 9

Solution :

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

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

Add (1) + (2), we get

3x + y - 2x - y = 7 + 9

x = 16

By applying x = 16 in (1) equation, we get

3(16) + y = 7

48 + y = 7

y = 7 - 48

y = -41

Therefore, the solution is x = 16 and y = -41.

Problem 2 :

4x + 3y = 2

2x - 3y = 1

Solution :

4x + 3y = 2 ---> (1)

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

Add (1) + (2), we get

4x + 3y + 2x - 3y = 2 + 1

6x = 3

x = 1/2

By applying x = 1/2 in (1) equation, we get

4(1/2) + 3y = 2

2 + 3y = 2

3y = 2 - 2

3y = 0

y = 0

Therefore, the  solution is x = 1/2 and y = 0.

Problem 3 :

2x + 2y = 3

x = 4y - 1

Solution :

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

x - 4y = -1 ---> (2)

(1) ∙ 2 ==> 4x + 4y = 6 ----> (3)

Add (3) + (2), we get

4x + 4y + x - 4y = 6 - 1

5x = 5

x = 1

By applying x = 1 in (1) equation, we get

2(1) + 2y = 3

2 + 2y = 3

2y = 3 - 2

2y = 1

y = 1/2

Therefore, the solution is x = 1 and y = 1/2.

Problem 4 :

y = 1 + x

2x + y = -2

Solution :

y = 1 + x

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

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

Add (1) + (2), we get

x - y + 2x + y = -1 - 2

3x = -3

x = -1

By applying x = -1 in equation (1)

y = 1 - 1

y = 0

Therefore, the solution is x = -1 and y = 0.

Problem 5 :

1/2x + 4y = 4

2x - y = 1

Solution :

1/2x + 4y = 4 ---> (1)

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

(1) ∙ 4 ==> 8x - 4y = 4 ---> (3)

Add (1) + (3), we get

1/2x + 4y + 8x - 4y = 4 + 4

17/2x = 8

17x = 16

x = 16/17

By applying x = 16/17 in equation (2)

2(16/17) - y = 1

32/17 - y = 1

-y = (17 - 32) / 17

-y = -15/17

y = 15/17

Therefore, the solution is x = 16/17 and y = 15/17.

Problem 6 :

y = x - 4

4x + y = 26

Solution :

y = x - 4

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

4x + y = 26 ---> (2)

Add (1) + (2), we get

x - y + 4x + y = 4 + 26

5x = 30

x = 6

By applying x = 6 in equation (1)

y = 6 - 4

y = 2

Therefore, the solution is x = 6 and y = 2.