document.write( "Question 1022479: Find the values of x and y that satisfy 3x − 1 + 2y = 0 and 3x2 - y2 + 4 = 0. Use the algebraic method to find the solution, and then use the graphing method to confirm whether the system of equations has real roots. \n" ); document.write( "

Algebra.Com's Answer #638145 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
{3x+2y = 1, 3x^2+4 = y^2}
\n" ); document.write( "

\r\n" );
document.write( "Solve 3x+2y = 1 for y\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute in\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute (-1+2i) in\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "One solution is (-1+2i, 2-3i)\r\n" );
document.write( "\r\n" );
document.write( "Substituting (-1-2i) the same way gives  2+3i\r\n" );
document.write( "\r\n" );
document.write( "So the other solution is (-1-2i, 2+3i)\r\n" );
document.write( "\r\n" );
document.write( "These solutions are complex imaginary, so the graphs\r\n" );
document.write( "should not cross:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And, as we see the black line, which is the graph of\r\n" );
document.write( ", does not cross the red hyperbola, which is\r\n" );
document.write( "the graph of   \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );