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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?

User Humphrey
by
8.2k points

2 Answers

0 votes

Answer:

infinitely many

Explanation:

just took the assignment for

User Balasubramanian
by
8.3k points
4 votes

Answer:

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

User Wouter Coekaerts
by
9.3k points

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