xy=6
x+y=13
x+y=13
minus x
y=13-x
sub for y in other equation
x(13-x)=6
13x-x^2=6
add -13x+x^2 to both sides
0=x^2-13x+6
use quadratic formula
for
ax^2+bx+c=0
x=[tex] \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} [/tex]
a=1
b=-13
c=6
x=[tex] \frac{-(-13)+/- \sqrt{(-13)^{2}-4(1)(6)} }{2(1)} [/tex]
x=[tex] \frac{13+/- \sqrt{169-24} }{2} [/tex]
x=[tex] \frac{13+/- \sqrt{145} }{2} [/tex]
x=[tex] \frac{13+ \sqrt{145} }{2} [/tex] or [tex] \frac{13- \sqrt{145} }{2} [/tex]
aprox
x=12.5208 or0.479203
the numbers are 12.5208 and 0.479203
