Question

Please help solve the system of equations

Answer 1

Answer:

(x, y) = ( 5, 6)

(x, y) = ( - 1, 0)

Step-by-step explanation:

$\begin{cases} y + x^2 - 5x = 6\\\\ y - x = 1\implies y = x + 1\end{cases}$

Plug $y = x +1$ in the equation $y + x^2 - 5x = 6$ we find:

$x + 1 + x^2 - 5x = 6$

$x^2 - 4x - 5=0$

$x^2 - 5x +x- 5=0$

$x(x - 5) +1(x- 5)=0$

$(x - 5) (x+1)=0$

$(x - 5) =0, \: (x+1)=0$

$x =5, \: x=-1$

$When \:x =5 \implies y =5+1=6$

(x, y) = ( 5, 6)

$When \:x =-1 \implies y =-1+1=0$

(x, y) = ( - 1, 0)