# I need help / complete solutions for 2 problems

• Jul 23rd 2008, 05:11 PM
norwoodjay
I need help / complete solutions for 2 problems
Give all solutions of each nonlinear systems of equations, including those with nonreal complex components.

x2+y2=10 x2+y2=4
2x2 -y2=17 2x-3y2=-12
• Jul 23rd 2008, 07:06 PM
norwoodjay
Two seperate problems
• Jul 23rd 2008, 07:12 PM
tutor
Hi,

solving the equation here
adding the equations here u will get
3x^2=27
x^2=9
x=3
and substitute x=3
y^2=10-9
y=1

multiplying 3 in first part then add both the equation
5x^2=0
x=0
when x=0 in first part then y=2

(Nerd)
• Jul 23rd 2008, 08:54 PM
Soroban
Hello, norwoodjay!

Quote:

Solve the systems of equations:

. . .x² + y² .= .10 . [1]
. . 2x² - y² .= .17 . [2]

Add [1] and [2]: .3x² = 27 . . x² = 9 . . x = ±3

Substitute into [1]: .(±3)² + y² .= .10 . . y² = 1 . . y = ±1

Solutions: .(3,1), (3,-1), (-3,1), (-3,-1)

Quote:

. . x² + y² .= . 4 .[1]
. .2x - 3y² .= -12 .[2]

Multiply [1] by 3: .3x² + 3y² .= .12
. . . . . . Add [2]: . 2x .- .3y² .= -12

And we have: .3x² + 2x .= .0 . . x(3x + 2) .= .0

. . Hence: .x .= .0, -2/3

Substitute into [1] and we get: .y .= .±2, ±4√2/3

Solutions: . (0, ±2), .(-2/3, ±4√2/3)

• Jul 24th 2008, 03:02 AM
norwoodjay
Thanks alot.