document.write( "Question 1059193: Solve the system of equations.
\n" ); document.write( "1.
\n" ); document.write( "y = x - 1
\n" ); document.write( "x^2 + y^2 = 25\r
\n" ); document.write( "\n" ); document.write( "2.
\n" ); document.write( "x + y = 1
\n" ); document.write( "y = x^2 - 5
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #674267 by math_helper(2461) $\"\"$ $\"About$

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\n" ); document.write( "1. Substitute \"x-1\" for \"y\" in the 2nd equation, to get:\r
\n" ); document.write( "\n" ); document.write( " $\"+x%5E2+%2B+%28x-1%29%5E2+=+25+\"$
\n" ); document.write( " $\"+x%5E2+%2B+%28x%5E2+-+2x+%2B+1%29+=+25+\"$
\n" ); document.write( " $\"++2x%5E2+-+2x+%2B+1+=+25+\"$
\n" ); document.write( " $\"++2x%5E2+-+2x+-+24+=+0+\"$
\n" ); document.write( " $\"+++x%5E2+-+x+-+12+=+0+\"$
\n" ); document.write( " $\"++%28x%2B3%29%28x-4%29+=+0+\"$
\n" ); document.write( "So x=-3 or x=4
\n" ); document.write( "x=-3 ==> y=-4
\n" ); document.write( "x=4 ==> y=3
\n" ); document.write( "Ч
\n" ); document.write( "Answer: (x,y) = (-3, -4) and (x,y) = (4,3)
\n" ); document.write( "Ч
\n" ); document.write( "Check:
\n" ); document.write( " $\"+%28-3%29%5E2+%2B+%28-4%29%5E2+=+9+%2B+16+=+25+\"$ (ok)
\n" ); document.write( "and
\n" ); document.write( " $\"+%284%29%5E2+%2B+%283%29%5E2+=+16+%2B+9+=+25+\"$ (ok)
\n" ); document.write( "ЧЧ\r
\n" ); document.write( "\n" ); document.write( "2. x+y = 1 ==> y=1-x
\n" ); document.write( "Substitute 1-x for y in the 2nd equation to get:\r
\n" ); document.write( "\n" ); document.write( " $\"+1-x+=+x%5E2+-+5+\"$
\n" ); document.write( " $\"+x%5E2+%2B+x+-+6+=+0+\"$
\n" ); document.write( " $\"+%28x-2%29%28x%2B3%29+=+0+\"$
\n" ); document.write( "x=2 or x=-3\r
\n" ); document.write( "\n" ); document.write( "x=2 ==> y=-1
\n" ); document.write( "x=-3 ==> y=4\r
\n" ); document.write( "\n" ); document.write( "Ч
\n" ); document.write( "Answer: (x,y) = (2,-1) and (x,y) = (-3,4)
\n" ); document.write( "Ч
\n" ); document.write( "Check:
\n" ); document.write( " $\"+2%5E2+-5+=+4-5+=+-1+\"$ (ok)
\n" ); document.write( " $\"+%28-3%29%5E2+-+5+=+9-5+=+4++\"$ (ok)\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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