Question

X-y=4+y
Xy=12
Find all solutions of the system of equations

Answer 1

\[x-y=4+y\iff x=4+2y\]

Answer 2

substitute in to the second equation, get\[(4+2y)y=12\]

Answer 3

multiply out, get
\[2y^2+4y=12\] or
\[y^2+2y=6\] or
\[y^2+2y-6=0\]

Answer 4

this does not factor, so you will need to use either the quadratic formula, or complete the square, to find \(y\)
since \(2\) is even, completing the square is easiest
\[y^2+2y=6\]
\[(y+1)^2=7\]
\[y+1=\pm\sqrt7\]
\[y=-1\pm\sqrt7\]

Answer 5

i assume the original problem is
\[x-y=4+y\\xy=12\] as posted, right?

Answer 6

Yes thank you :)