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

2 Answers
Dec 5, 2017

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

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