Question

How do you solve the system of equations `6x + 3y = - 16` and `6x-y=4`?

Answer 1

`x=-1/6` and `y=-5`

Explanation:

To solve this system with two unknowns we have to get rid of one unknown and find the value of the second then substitute it in one of the equations to compute the value of the one we got rid of before .

`6x+3y=-16` eq(1)
`6x-y=4` eq(2)

Let us multiply eq(2) by `-1` so we get rid of `x`:

`6x+3y=-16` eq(1)
`-6x+y=-4` eq(2)

Let's add both equations we have:

`eq(1)+eq(2)`
`rArr6x+3y-6x+y=-16-4`
Grouping same unknowns :

`rArr6x-6x+3y+y=-20`
`rArr0*x+4y=-20`
`rArr4y=-20`
`rArry=-20/4`
`rArrcolor(blue)(y=-5)`

Let us substitute the value of `y` in eq(1) to find `x`we have:

`6x+3y=-16`
`rArr6x+3(-5)=-16`
`rArr6x-15=-16`
`rArr6x=-16+15`
`rArr6x=-1`
`rArrcolor(blue)(x=-1/6`

Let us check the value by substituting the values of `x` and `y` in eq(2):

`6x-y=?4`
`rArr6(-1/6)-(-5)=?4`
`rArr-1+5=?4`
`rArr4=?4` true so `x=-1/6` and `y=-5` verifies the equation.