Question

Please help
solve the system of equations

Answer 1

(x, y) = ( 5, 6)

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

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)