Solve system of equations

Question

$$\sin(x+y)+1.6x=0$$

$$x^2+y^2=-1$$

Can this system be solved? Please help me with it. I managed to make graphs of it but can't get it solved without graph.

Graph:

Answer 1

Hint: For what real $x$ and $y$ will we have $$x^2+y^2=-1,$$ if any?

Answer 2

If the domain is real number no square numbers sum will be negative.

So no x and y satisfy the equation

Answer 3

since we have for all real numbers $x^2+y^2\geq 0>-1$ we get no real solutions for this system. you can only plug $y=\sqrt{-x^2-1}$ or $y=-\sqrt{-x^2-1}$ in your equation.

Answer 4

Solved:
$$sin(x+y)+1.6x=0$$ $$x^2+y^2=-1$$
$$y=√(|-x^2-1|)$$

$$ sin(x+√(|-x^2-1|)+1.6*x=0$$

x=-0.393536

$$ y=√(|0.393536^2-1|)$$

y=0.91931

Looking at the graph it seems these are correct values. Thank you, especially Dr. Sonnhard Graubner.