Question 935314

The sum of two number is {{{30}}}
{{{x+y=30}}}....eq.1

 and the difference of their square is {{{180}}}

{{{x^2-y^2=180}}}....eq.2

find the numbers: 

{{{x+y=30}}}....eq.1...solve for {{{x}}}

{{{x=30-y}}}...substitute in eq.2

{{{(30-y)^2-y^2=180}}}....eq.2...solve for {{{y}}}


{{{900-60y+cross(y^2)-cross(y^2)=180}}}

{{{900-60y=180}}}

{{{900-180=60y}}}

{{{720=60y}}}

{{{720/60=y}}}

{{{highlight(y=12)}}}

now find {{{x}}}

{{{x=30-y}}}

{{{x=30-12}}}

{{{highlight(x=18)}}}