Question

Solve the following system algebraically. y = x2 – 9x + 18 y = x – 3

Answer 1

`y=x^2-9x+18.....(1)\\y=x-3........(2)\\\mathrm{Equating\ equation(1) \ and\ (2),}\\x-3=x^2-9x+18\\\mathrm{or,\ }x^2-10x+21=0\\\mathrm{or,\ }x^2-7x-3x+21=0\\\mathrm{or,\ }x(x-7)-3(x-7)=0\\\mathrm{or,\ }(x-7)(x-3)=0\\\mathrm{i.e. \ }x=7\ \mathrm{or}\ 3.\\\mathrm{When\ }x=7,y=7-3=4.\\\mathrm{When\ }x=3, y=3-3=0`