Elimination

Question

1) 6j+4k=-46, 2j+4k=-26?

2) 8x+y=27, -3x+4y=3?

Answer 1

1)

Given equations are

6j + 4k = -46   ------------- (1)

2j + 4k = -26   ------------- (2)

From equation (1)

6j + 4k = -46 ⇒ 4k = - 46 - 6j

From equation (2)

2j + 4k = -26 ⇒ 4k = - 26 - 2j

Substitute 4k = - 46 - 6j in above equation

- 46 - 6j = - 26 - 2j

-46 + 26 = 6j - 2j

4j = 20

j = 5

Substitute j = 5 in equation 4k = - 26 - 2j

4k = -26 - 2*5

4k = -26 - 10

4k = -36

k = - 9

Solution is j = 5 and k = - 9

Answer 2

2)

Given equations are

8x+y=27         ------------- (1)

-3x+4y=3       -------------- (2)

From equation (1)

8x+y=27 ⇒ y = 27 - 8x

Substitute y = 27 - 8x for eliminate y in above equation (2)

-3x+4(27 - 8x)=3

-3x + 108 - 32x = 3

-35x  + 108 = 3

35x = 108 - 3

35x = 105

x = 105/3

x = 3

Substitute x = 3 in equation y = 27 - 8x

y = 27 - 8*3

y = 27 - 24

y = 3

Solution is x = 3 and y = 3