Question

1/2x + 1/3y = 0

1/4x -1/2 y = 8
What is the solution of the system shown?
(-8, 12)
(8, -12)
(8, 12)

Answer 1

(8,-12) the second option :)

Explanation:

Answer 2

`(8,-12)`

Explanation:

The two equations are:

`(1)/(2)x+(1)/(3)y=0\\(1)/(4)x-(1)/(2)y=8`

We can solve the first equation for
`x` and then substitute into second equation to find the value of
`y`.

`(1)/(2)x+(1)/(3)y=0\\(1)/(2)x=-(1)/(3)y\\x=(-(1)/(3)y)/((1)/(2))\\x=-(2)/(3)y`

Now,

`(1)/(4)x-(1)/(2)y=8\\(1)/(4)(-(2)/(3)y)-(1)/(2)y=8\\-(2)/(12)y-(1)/(2)y=8\\-(2)/(3)y=8\\y=(8)/(-(2)/(3))\\y=-12`

Substituting
`y=-12` into the "solved for
`x`" version of first equation, we get the value of
`x`. So,

`x=-(2)/(3)y\\x=-(2)/(3)(-12)\\x=8`

Hence the ordered pair is
`(8,-12)` and this is the solution to the system of equations shown.