Math Help Forum: 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

Two seperate problems

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

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

Hello, norwoodjay!

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)

. . 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)

Thanks alot.