Question

Find all solutions to the non-linear systems: 4`sqrtx` + `sqrty` = 34 and `sqrtx` + 4`sqrty` = 16 ?

Answer 1

x=64
y=4

Explanation:

if
`sqrt(x)=a`
`sqrt(y)=b`
then
`4a+b=34`
`a+4b=16`
multyply the first equation by -1; the second by 4 and add them together. Then you get

`15b = 64-34`
`b=30/15=2`
Now. Let's go back to find a.
4a+b=34 so after substitating b=2 you get:
`a=32/4=8`

then back:
`sqrt(x)=a`
`sqrt(x)=8`
`x=8^2=64`

`sqrt(y)=b`
`sqrt(y)=2`
`y=2^2=4`

Answer 2

the answers are `:.x=64 and y=4`

Explanation:

the equations are `4sqrtx+sqrty=34->(1)`
`sqrtx+4sqrty=16->(2)`
multiplying `(2) by -4` we get
`-4sqrtx-16sqrty=-64->(3)`
solving `(2) + (3)`
`4sqrtx+sqrty-4sqrtx-16sqrty=-64+34rArr-15sqrty=-30rArrsqrty=2rArry=4`
put `y=4` in `(1)` we get `4sqrtx+2=34rArr4sqrtx=32rArrsqrtx=8rArrx=64`