Question 985971
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You need to find two integers &nbsp;<B>x</B>&nbsp; and &nbsp;<B>y</B>&nbsp; from the system of two equations in two unknowns


{{{system(x + y = 3,
x*y = -40)}}}.


Express &nbsp;<B>y</B>&nbsp; from the first equation &nbsp;y = 3 - x &nbsp;and substitute it to the second equation. &nbsp;You will get 


x*(3 - x) = -40.


Solve it:


{{{-x^2}}} + {{{3x}}} + {{{40}}} = {{{0}}},


{{{x^2}}} - {{{3x}}} - {{{40}}} = {{{0}}},


The roots are &nbsp;x = 8 &nbsp;and &nbsp;x = -5 &nbsp;&nbsp;(use the quadratic formula).


From the first equation, &nbsp;if &nbsp;x = 8 &nbsp;then &nbsp;y = -5.

Similarly, &nbsp;if &nbsp;x = -5, &nbsp;then &nbsp;y = 8.


<B>Answer</B>. &nbsp;The pairs &nbsp;(8,-5) &nbsp;and &nbsp;(-5,8) &nbsp;are the solutions.