Question

What two numbers add to 9 and multiply to -70

Answer 1

x, y - the numbers

The numbers add to 9 and multiply to -70.

`x+y=9 \\ xy=-70 \\ \\ y=9-x \\ xy=-70 \\ \\ \hbox{substitute 9-x for y in the second equation:} \\ x(9-x)=-70 \\ 9x-x^2=-70 \\ -x^2+9x+70=0 \\ -x^2+14x-5x+70=0 \\ -x(x-14)-5(x-14)=0 \\ (-x-5)(x-14)=0 \\ -x-5=0 \ \lor \ x-14=0 \\ x=-5 \ \lor \ x=14 \\ \\ y=9-x \\ y=9-(-5) \ \lor \ y=9-14 \\ y=14 \ \lor \ y=-5 \\ \\ (x,y)=(-5,14) \hbox{ or } (x,y)=(14,-5)`

The numbers are -5 and 14.