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Say I have this equation: $$x^2=y \quad y^3=x \quad x=y^{1/2}$$

and say I wanted to turn them into a single equation so they will be graphed from just one equation. I tried multiplying them and making them equal to zero, no hope. I even tried to search "super-imposing" on Google, no help.

gt6989b
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1 Answers1

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So you have a system of equations $$x^2=y \quad y^3=x \quad x=y^{1/2}$$ and I understand that you want one equation with the same solution set as this system. What you can do is: $$(x^2-y)^2+(y^3-x)^2+(x-y^{1/2})^2=0$$ Assuming only real numbers, this equation is solved if and only if all three terms are zero, which is exactly your system of equations.

Arnaud Mortier
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  • but what if I multiplied the equations by sqrt(|x|/x)? will it break? –  Feb 25 '19 at 17:37