Question

6x − y + z = −3
4x − 3z = −13
2y + 5z = 15
Find the solutions?

Answer 1

The solution of the equation are x = - 1 , y = 0 and z = 3

Explanation:

Given three linear equation as :

6 x - y + z = - 3 ......A

4 x - 3 z = - 13 ......B

2 y + 5 z = 15 ......C

Solving eq A and C

I.e 2× (6 x - y + z ) = -3 ×2

or, 12 x - 2 y + 2 z = - 6

So, ( 12 x - 2 y + 2 z ) + ( 2 y + 5 z) = - 6 + 15

Or, 12 x + 7 z = 9 ......D

Solving eq B and D

I.e 3 × ( 4 x - 3 z ) = - 13 × 3

or, 12 x - 9 z = - 39

So, ( 12 x + 7 z ) - ( 12 x - 9 z ) = 9 + 39

or, 16 z = 48

∴ z =
`(48)/(16)`

i.e z = 3

put the value of z in eq D

So, 12 x + 7×3 = 9

Or, 12 x = 9 - 21

or, 12 x = - 12

∴ x = -
`(12)/(12)`

I.e x = - 1

Now, Put The value of z in eq C

or, 2 y + 5 z = 15

or, 2 y + 5 × 3 = 15

Or, 2 y = 15 - 15

or, 2 y = 0

∴ y = 0

Hence The solution of the equation are x = - 1 , y = 0 and z = 3 Answer