Question

If the ordered pairs (x²-1,y+3) and (3,x+4) are equal, find |x| and |y|

Answer 1

Dear Student,

$$\begin{gathered} Astheorderedpairsareequal. \\ {x}^2-1=3\Rightarrow x^2=4 \\ x=\pm 2 \\ Alsoy+3=x+4\Rightarrow y=x+1 \\ Thusvalueofof\left|x\right|=2 \\ andvalueof\left|y\right|=\left|x+1\right|=\left|2+1\right|(puttingx=2)weget\left|y\right|=3 \\ andputtingx=-2,y=\left|-2+1\right|\Rightarrow \left|-1\right| \\ \left|y\right|=1 \\ Hencevalueof\left|x\right|=2and\left|y\right|=1and\left|y\right|=3 \end{gathered}$$
Regards,