Question 1059193

1.   Substitute "x-1" for "y" in the 2nd equation, to get:

 {{{ x^2 + (x-1)^2 = 25 }}}
{{{ x^2 + (x^2 - 2x + 1) = 25 }}}
{{{  2x^2 - 2x + 1 = 25 }}}
{{{  2x^2 - 2x - 24 = 0 }}}
{{{   x^2 - x - 12 = 0 }}}
{{{  (x+3)(x-4) = 0 }}}
So x=-3  or x=4
x=-3 ==>  y=-4
x=4 ==> y=3
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Answer:   (x,y) = (-3, -4)  and  (x,y) = (4,3)
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Check:
    {{{ (-3)^2 + (-4)^2 = 9 + 16 = 25 }}}  (ok)
and
    {{{ (4)^2 + (3)^2 = 16 + 9 = 25 }}}  (ok)
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2.   x+y = 1 ==> y=1-x
Substitute 1-x for y in the 2nd equation to get:

  {{{ 1-x = x^2 - 5 }}}
  {{{ x^2 + x - 6 = 0 }}}
  {{{ (x-2)(x+3) = 0 }}}
x=2  or  x=-3

x=2 ==> y=-1
x=-3 ==> y=4

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Answer:  (x,y) = (2,-1)  and (x,y) = (-3,4)
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Check:
           {{{ 2^2 -5 = 4-5 = -1 }}}   (ok)
           {{{ (-3)^2 - 5 = 9-5 = 4  }}}  (ok)