Question Number 207270 by hardmath last updated on 10/May/24
$$\begin{cases}{\mid\mathrm{x}\mid\:+\:\mathrm{y}\:−\:\mathrm{1}\:=\:\mathrm{0}}\\{\mathrm{x}\:−\:\mathrm{y}\:−\:\mathrm{1}\:=\:\mathrm{0}}\end{cases}\:\:\:\mathrm{find}:\:\:\mathrm{2x}−\mathrm{3y}\:=\:? \\ $$
Answered by A5T last updated on 10/May/24
$${y}=\mathrm{1}−\mid{x}\mid={x}−\mathrm{1} \\ $$$$\Rightarrow{x}+\mid{x}\mid=\mathrm{2}\Rightarrow\sqrt{{x}^{\mathrm{2}} }=\mathrm{2}−{x}\Rightarrow{x}^{\mathrm{2}} =\mathrm{4}+{x}^{\mathrm{2}} −\mathrm{4}{x} \\ $$$$\Rightarrow{x}=\mathrm{1}\Rightarrow{y}=\mathrm{0}\Rightarrow\mathrm{2}{x}−\mathrm{3}{y}=\mathrm{2} \\ $$
Commented by hardmath last updated on 10/May/24
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dear}\:\mathrm{professor} \\ $$