Answer:
The system has infinitely solutions
Step-by-step explanation:
we have
[tex]-\frac{1}{3}x^{2}=-\frac{5}{6}+\frac{1}{3}y^{2}[/tex]
[tex]\frac{1}{3}x^{2}+\frac{1}{3}y^{2}=\frac{5}{6}[/tex]
Multiply by 3 both sides
[tex]x^{2}+y^{2}=\frac{5}{2}[/tex] ----> equation A
The equation A is a circle centered at origin with radius [tex]r=\sqrt{5/2}\ units[/tex]
and
[tex]5y^{2} =\frac{25}{2}-5x^{2}[/tex]
[tex]5x^{2}+5y^{2} =\frac{25}{2}[/tex]
Divide by 5 both sides
[tex]x^{2}+y^{2} =\frac{5}{2}[/tex] ----> equation B
The equation B is a circle centered at origin with radius [tex]r=\sqrt{5/2}\ units[/tex]
Equation A and Equation B are the same
Therefore
The system has infinitely solutions
Answer:
infinitely many
Step-by-step explanation:
just took the assignment for
