document.write( "Question 1181988: Solve the following equations.
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\n" ); document.write( " {x² + y² = 2 \n" ); document.write( "

Algebra.Com's Answer #811950 by ikleyn(52769) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Regarding the first system of two equations,\r\n" );
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document.write( "express x = -2y  from the first equation and substitute to the second equation,\r\n" );
document.write( "replacing x there.\r\n" );
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document.write( "You will get then\r\n" );
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document.write( "    (2y)^2 + y^2 = 5\r\n" );
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document.write( "     4y^2  + y^2 = 5\r\n" );
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document.write( "         5y^2    = 5\r\n" );
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document.write( "          y^2    = 1\r\n" );
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document.write( "          y      =  = +/- 1.\r\n" );
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document.write( "Thus you obtain two solutions:\r\n" );
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document.write( "    a)  for y = 1,   x = -2y = -2.\r\n" );
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document.write( "    b)  for y = -1,  x = -2y = 2.\r\n" );
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document.write( "ANSWER.  There are two solutions  (x,y) = (-2,1)  and  (x,y) = (2,-1).\r\n" );
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document.write( "These two solutions are two intersection points of the straight line  x + 2y = 0  and  the circle  x^2 + y^2 = 5. \r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and carefully explained.\r
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Solving systems of algebraic equations of degree 2 and degree 1 \r
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\n" ); document.write( "\n" ); document.write( "Solve the second system of equations similarly.\r
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\n" ); document.write( "\n" ); document.write( "Do not post more than one problem in one post --- it is PROHIBITED by the rules of this forum.\r
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\n" ); document.write( "\n" ); document.write( "Post them SEPARATELY.\r
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