We need to clear first in one equation any of the variables:
Lest take the first one:
[tex]x+y=12[/tex][tex]x=12-y[/tex]We replace this value of x in the other equation:
[tex](12-y)\cdot\text{ y = -64}[/tex][tex]12y-y^2=\text{ -64}[/tex]then organizing we have
[tex]-y^2+12y+64=0[/tex]Using the quadratic equation we obtain:
[tex]y=\frac{-12\pm\sqrt[]{12^2-4(-1)(64)}}{2(-1)}[/tex][tex]y=\frac{-12\pm\sqrt[]{144+256}}{-2}[/tex][tex]y=\frac{-12\pm\sqrt[]{400}}{-2}[/tex][tex]y=\frac{-12\pm20}{-2}[/tex]we have two possible solution, one with the addition and one with the subtration
[tex]y_1=\frac{-12+20}{-2}=\frac{8}{-2}=-4[/tex][tex]y_2=\frac{-12-20}{-2}=\frac{-32}{-2}=-16[/tex]Using that values in the first equation when we clear the x:
[tex]x_1=12-y_1=\text{ 12 - (-4) =16}[/tex][tex]x_2=12-y_2=\text{ 12 - (-16) =28}[/tex]So if we can see those values in the equation x • y = -64
[tex]x_1\cdot y_1=-64_{}[/tex][tex]16\cdot(-4)=-64[/tex]If you try to do this multiply with x2 y y2 it will be a different number s
The answer is X= 16 y Y= - 4
