Question

Solve the system of equations please?

Answer 1

See below.

Explanation:

Making `y = lambda x`

`{(1+4lambda^2=5 lambda),(x^2(2-lambda^2)=31):}`

or

#((lambda = 1/4, x = -4),(lambda = 1/4, x = 4),(lambda = 1, x = -sqrt[31]),(lambda = 1, x = sqrt[31]))#

and then

#((y = -1, x = -4),(y = 1, x = 4),(y = -sqrt(31), x = -sqrt[31]),(y= sqrt(31), x = sqrt[31]))#

Answer 2

`(2,-44/31)`, `(-2,44/31)`, `(sqrt31,sqrt31)`, `(-sqrt31,-sqrt31)`

Explanation:

from equation (1) we have
`x^2+4y^2=5xy` .............................(3)
now multiply equation (2) by 4, i.e
`8x^2-4y^2=124` .............................(4)
now adding equation (3) and (4), we get
`9x^2=5xy+124`
`9x^2-124=5xy`
`(9x^2-124)/"5x"=y` ................................(5)
now substitute equation (5) in equation 2 and by solving , we get
`x^4-47x^2+496=0` ................................(6)
solving equation (6) we get
`x=2, -2, sqrt31, -sqrt31`
now using these values in equation (6), we get
`y=-44/5, 44/5, sqrt31, -sqrt31` respectively.