Question

What is the value of w in the solution to the following system of linear equations?

5v+4w=1
3v-6w=2

A) - 7/18
B) - 1/6
C) - 1/9
D) 1/3

Answer 1

>>>>w = - 1 / 6<<<<

Answer 2

For this case we have a system of two linear equations with two igcognitas, given by:

`5v + 4w = 1\\3v-6w = 2`

Where v and w are the unknowable variables.

To solve, we perform the following steps:

1st step:

We multiply the first equation by 3:

`15v + 12w = 3`

2nd step:

We multiply the second equation by -5:

`-15v + 30w = -10`

3rd step:

We add the equations:

`15v + 12w = 3\\-15v + 30w = -10`

We have then:

`42w = -7`

`w =-(7)/(42)`

`w =-(1)/(6)`

Thus, the value of w is
`-(1)/(6)`.

4th step:

We substitute
`w =-(1)/(6)` in any of the equations:

`3v-6w = 2\\3v-6 * (-(1)/(6)) = 2`

`3v + 1 = 2\\3v = 2-1\\3v = 1`

`v =(1)/(3)`

So, the value of v is
`(1)/(3)`

Answer:

The value of w is
`-(1)/(6)`