Question

Solve the system of equations algebraically:

x^2+y^2=10

y+3x^2=0


I've tried everything and I know that I need to solve this by substitution but I can't figure out how to get rid of the exponent in the second equation so that I can plug it into the first. Please help :(

Answer 1

Answer; y=10/3
x= - i radical 10/3

Step - by - step

y= -3x^2
x^2 + y^2 = 10
Replace all occurrences of y in

x^2 + (-3x^2)^2 = 10
x^2 + 9x^4 = 10

Substract 10 from both sides of the equation

x^2 + 9x^4 - 10 = 0

Factor the left side
(x + 1 ) ( x - 1 ) ( 9x^4 - 10 ) =0
x + 1= 0
x = - 1

x - 1 = 0
x = 1

9x^2 + 10 = 0
x^2 = - 10/9
x = +- radical -10/9
x = +- i radical 10/3

y = - 3x^2
y = - 3 ( i radical 10/3 )^2
y = 10/3