document.write( "Question 50218: Solve the following system of equations:
\n" ); document.write( "3x^2+4xy-2y^2=2
\n" ); document.write( "3x+2y=-10 \n" ); document.write( "
Algebra.Com's Answer #33351 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Solve the following system of equations:\r\n" );
document.write( "\r\n" );
document.write( "                         3x² + 4xy - 2y² = 2 \r\n" );
document.write( "                                 3x + 2y = -10 \r\n" );
document.write( "\r\n" );
document.write( "Solve the second equation for either of the unknowns.\r\n" );
document.write( "I'll pick x:\r\n" );
document.write( "\r\n" );
document.write( "                                 3x + 2y = -10\r\n" );
document.write( "\r\n" );
document.write( "add -2y to both sides\r\n" );
document.write( "\r\n" );
document.write( "                                      3x = -10 - 2y\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 3\r\n" );
document.write( "             \r\n" );
document.write( "                                       x = (-10 - 2y)/3                                  \r\n" );
document.write( "factor out -2\r\n" );
document.write( "\r\n" );
document.write( "                                       x = -2(5 + y)/3\r\n" );
document.write( "           \r\n" );
document.write( "In the first original equation,\r\n" );
document.write( "\r\n" );
document.write( "                         3x² + 4xy - 2y² = 2\r\n" );
document.write( "\r\n" );
document.write( "substitute -2(5 + y)/3 for x\r\n" );
document.write( "\r\n" );
document.write( " 3[-2(5 + y)/3]² + 4[-2(5 + y)/3]y - 2y² = 2\r\n" );
document.write( "\r\n" );
document.write( "  3[4(5 + y)²/9] + 4y[-2(5 + y)/3] - 2y² = 2\r\n" );
document.write( "\r\n" );
document.write( "         4(5 + y)²/3 - 8y(5 + y)/3 - 2y² = 2\r\n" );
document.write( "\r\n" );
document.write( "4(25 + 10y + y²)/3 - (40y + 8y²)/3 - 2y² = 2\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by 3 to clear of fractions:\r\n" );
document.write( "\r\n" );
document.write( "    4(25 + 10y + y²) - (40y + 8y²) - 6y² = 6\r\n" );
document.write( "\r\n" );
document.write( "       100 + 40y + 4y² - 40y - 8y² - 6y² = 6\r\n" );
document.write( "\r\n" );
document.write( "Collect terms \r\n" );
document.write( "\r\n" );
document.write( "                              100 - 10y² = 6\r\n" );
document.write( "\r\n" );
document.write( "Get 0 on the right\r\n" );
document.write( "\r\n" );
document.write( "                               94 - 10y² = 0\r\n" );
document.write( "\r\n" );
document.write( "Divide thru by 2                47 - 5y² = 0  \r\n" );
document.write( "\r\n" );
document.write( "                                    -5y² = -47\r\n" );
document.write( "\r\n" );
document.write( "                                      y² = 47/5\r\n" );
document.write( "                                             ____\r\n" );
document.write( "                                       y = ±Ö47/5\r\n" );
document.write( "                                             ___\r\n" );
document.write( "Rationalize denominator                y = ±Ö235/5  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute into                  3x + 2y = -10 \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Using the + value\r\n" );
document.write( "                                 ___\r\n" );
document.write( "                         3x + 2(Ö235/5) = -10\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by 5\r\n" );
document.write( "                                     ___\r\n" );
document.write( "                             15x + 2Ö235 = -50  \r\n" );
document.write( "                                           ___\r\n" );
document.write( "                             15x = -50 - 2Ö235                                \r\n" );
document.write( "                                            ___\r\n" );
document.write( "                               x = (-50 - 2Ö235)/15\r\n" );
document.write( "                                            ___ \r\n" );
document.write( "                               x = -2(25 + Ö235)/15                \r\n" );
document.write( "\r\n" );
document.write( "So one solution is \r\n" );
document.write( "                    ___       ___\r\n" );
document.write( "(x, y) = ( -2(25 + Ö235)/15, Ö235/5 )\r\n" );
document.write( "\r\n" );
document.write( "----------------------------------------             \r\n" );
document.write( "\r\n" );
document.write( "Using the - value\r\n" );
document.write( "                                  ___\r\n" );
document.write( "                         3x + 2(-Ö235/5) = -10\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by 5\r\n" );
document.write( "                                     ___\r\n" );
document.write( "                             15x - 2Ö235 = -50  \r\n" );
document.write( "                                           ___\r\n" );
document.write( "                             15x = -50 + 2Ö235                                \r\n" );
document.write( "                                            ___\r\n" );
document.write( "                               x = (-50 + 2Ö235)/15\r\n" );
document.write( "                                            ___ \r\n" );
document.write( "                               x = -2(25 - Ö235)/15                \r\n" );
document.write( "\r\n" );
document.write( "So the other solution is \r\n" );
document.write( "                    ___        ___\r\n" );
document.write( "(x, y) = ( -2(25 - Ö235)/15, -Ö235/5 )\r\n" );
document.write( "\r\n" );
document.write( "Tell your teacher I said he or she is a meany for giving you such a \r\n" );
document.write( "messy problem.  It is messy enough as it is. However, if you solve for\r\n" );
document.write( "y first instead of x, the problem is even messier, in fact a lot\r\n" );
document.write( "messier.  That was the first way I did it!!  Also there is no way to\r\n" );
document.write( "tell in advance which way is going to be messier.  Your teacher needs\r\n" );
document.write( "a spanking!!  :-)\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );