document.write( "Question 44277: Can you solve x in terms of y and y in terms of x for the following equation:
\n" ); document.write( "3y² + 4xy - 9x² = -1\r
\n" ); document.write( "\n" ); document.write( "Thank You
\n" ); document.write( "acrown1@umbc.edu \n" ); document.write( "
Algebra.Com's Answer #29185 by AnlytcPhil(1806) $\"\"$ $\"About$
You can put this solution on YOUR website!
Can you solve x in terms of y and y in terms of x \r\n" );
document.write( "for the following equation:\r\n" );
document.write( "\r\n" );
document.write( "3y² + 4xy - 9x² = -1\r\n" );
document.write( "\r\n" );
document.write( "Yes with the quadratic formula:\r\n" );
document.write( "\r\n" );
document.write( "To solve for y in terms of x\r\n" );
document.write( "\r\n" );
document.write( "3y² + 4xy - 9x² = -1\r\n" );
document.write( "\r\n" );
document.write( "Get 0 on the right\r\n" );
document.write( "\r\n" );
document.write( "3y² + 4xy + 1 - 9x² = 0\r\n" );
document.write( "\r\n" );
document.write( "Now we write it this way\r\n" );
document.write( "\r\n" );
document.write( "(3)y² + (4x)y + (1 - 9x²) = 0\r\n" );
document.write( "\r\n" );
document.write( "so you can compare it with\r\n" );
document.write( "\r\n" );
document.write( "  Ay² + By + C = 0\r\n" );
document.write( "\r\n" );
document.write( "A = 3, B = 4x and C = (1 - 9x²)\r\n" );
document.write( "\r\n" );
document.write( "               ___________________\r\n" );
document.write( "      -(4x) ± Ö(4x)²-4(3)(1 - 9x²)\r\n" );
document.write( "y = -------------------------------\r\n" );
document.write( "              2(3) \r\n" );
document.write( "\r\n" );
document.write( "             ________________\r\n" );
document.write( "      -4x ± Ö16x²-12(1 - 9x²)\r\n" );
document.write( "y = -------------------------------\r\n" );
document.write( "              6\r\n" );
document.write( "\r\n" );
document.write( "             _______________\r\n" );
document.write( "      -4x ± Ö16x²-12 + 108x²\r\n" );
document.write( "y = --------------------------\r\n" );
document.write( "              6\r\n" );
document.write( " \r\n" );
document.write( "             ________\r\n" );
document.write( "      -4x ± Ö124x²-12 \r\n" );
document.write( "y = ---------------------\r\n" );
document.write( "              6\r\n" );
document.write( "\r\n" );
document.write( "             __________\r\n" );
document.write( "      -4x ± Ö4(31x²-3) \r\n" );
document.write( "y = ---------------------\r\n" );
document.write( "              6\r\n" );
document.write( "              ______\r\n" );
document.write( "      -4x ± 2Ö31x²-3 \r\n" );
document.write( "y = ------------------\r\n" );
document.write( "              6\r\n" );
document.write( "\r\n" );
document.write( "               ______\r\n" );
document.write( "      2(-2x ± Ö31x²-3) \r\n" );
document.write( "y = ------------------\r\n" );
document.write( "            6\r\n" );
document.write( "\r\n" );
document.write( "      1         ______\r\n" );
document.write( "      2(-2x ± Ö31x²-3) \r\n" );
document.write( "y = ------------------\r\n" );
document.write( "            6\r\n" );
document.write( "            3\r\n" );
document.write( "\r\n" );
document.write( "             ______\r\n" );
document.write( "      -2x ± Ö31x²-3) \r\n" );
document.write( "y = ------------------\r\n" );
document.write( "           3\r\n" );
document.write( "\r\n" );
document.write( "That's y solved in terms of x\r\n" );
document.write( "\r\n" );
document.write( "To solve for x in terms of y:\r\n" );
document.write( "\r\n" );
document.write( "3y² + 4xy - 9x² = -1\r\n" );
document.write( "\r\n" );
document.write( "Get 0 on the right\r\n" );
document.write( "\r\n" );
document.write( "3y² + 4xy + 1 - 9x² = 0\r\n" );
document.write( "\r\n" );
document.write( "Now we write it this way\r\n" );
document.write( "\r\n" );
document.write( "-9x² + 4yx + 1 + 3y² = 0\r\n" );
document.write( "\r\n" );
document.write( "Multiply thru by -1 because it's\r\n" );
document.write( "easier when the squared term is \r\n" );
document.write( "positive:\r\n" );
document.write( "\r\n" );
document.write( "9x² - 4yx - 1 - 3y² = 0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(9)x² + (-4y)x + (-1 - 3y²) = 0\r\n" );
document.write( "\r\n" );
document.write( "so you can compare it with\r\n" );
document.write( "\r\n" );
document.write( "  Ax² + Bx + C = 0\r\n" );
document.write( "\r\n" );
document.write( "A = 9, B = -4y and C = (-1 - 3y²)\r\n" );
document.write( "\r\n" );
document.write( "I'll let YOU solve this, and the answer is\r\n" );
document.write( "            ______\r\n" );
document.write( "      2y ± Ö31y²+9) \r\n" );
document.write( "x = ------------------\r\n" );
document.write( "           9\r\n" );
document.write( "\r\n" );
document.write( "That's x solved in terms of y\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( " \n" ); document.write( "
\n" );