Answer:
(x, y) = ( 5, 6)
(x, y) = ( - 1, 0)
Step-by-step explanation:
[tex] \begin{cases} y + x^2 - 5x = 6\\\\ y - x = 1\implies y = x + 1\end{cases} [/tex]
Plug [tex] y = x +1 [/tex] in the equation [tex] y + x^2 - 5x = 6[/tex] we find:
[tex] x + 1 + x^2 - 5x = 6[/tex]
[tex] x^2 - 4x - 5=0[/tex]
[tex] x^2 - 5x +x- 5=0[/tex]
[tex] x(x - 5) +1(x- 5)=0[/tex]
[tex] (x - 5) (x+1)=0[/tex]
[tex] (x - 5) =0, \: (x+1)=0[/tex]
[tex] x =5, \: x=-1[/tex]
[tex] When \:x =5 \implies y =5+1=6 [/tex]
(x, y) = ( 5, 6)
[tex] When \:x =-1 \implies y =-1+1=0 [/tex]
(x, y) = ( - 1, 0)
