Question 743011
Given:
{{{ x^2 + y = 3 }}} [1]
{{{ x + y = 1 }}} [2]

Subtracting x^2 from both sides of  [1] gives {{{ y= 3 - x^2 }}} [3]
Subtracting x from both sides of [2] gives {{{ y = 1-x }}} [4]

Combining [3] and [4] {{{ y = 3 - x^2 = 1-x }}}
Thus {{{ x^2 -x -2 = 0 }}}


Factorising gives {{{ (x-2)(x+1) = 0 }}}


Hence x=2 or x = -1


Subst x=2 in [3] gives {{{ y = 3- 2^2 =-1 }}}
Subst x=-1 in [3] gives {{{ y = 3 - (-1)^2 = 3-1 = 2 )))


Checking:
Subst x=2 in [4] gives {{{ y = 1-2 = -1 }}}
Subst x=-1 in [4] gives {{{ y = 1-x = 2 }}}


Hence the solutions are (2,-1) and (-1,2)