Question

Consider the following system of equations:

-1/3x^2 = -5/6 + 1/3y^2 and
5y^2 = 25/2 - 5x^2
How many solutions does the system have?

Answer 1

infinitely many

Explanation:

just took the assignment for

Answer 2

The system has infinitely solutions

Explanation:

we have

`-(1)/(3)x^(2)=-(5)/(6)+(1)/(3)y^(2)`

`(1)/(3)x^(2)+(1)/(3)y^(2)=(5)/(6)`

Multiply by 3 both sides

`x^(2)+y^(2)=(5)/(2)` ----> equation A

The equation A is a circle centered at origin with radius
`r=√(5/2)\ units`

and

`5y^(2) =(25)/(2)-5x^(2)`

`5x^(2)+5y^(2) =(25)/(2)`

Divide by 5 both sides

`x^(2)+y^(2) =(5)/(2)` ----> equation B

The equation B is a circle centered at origin with radius
`r=√(5/2)\ units`

Equation A and Equation B are the same

Therefore

The system has infinitely solutions