# SOLUTION: Can you solve x in terms of y and y in terms of x for the following equation: 3y² + 4xy - 9x² = -1 Thank You acrown1@umbc.edu

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 Click here to see ALL problems on Equations Question 44277: Can you solve x in terms of y and y in terms of x for the following equation: 3y² + 4xy - 9x² = -1 Thank You acrown1@umbc.eduAnswer by AnlytcPhil(1277)   (Show Source): You can put this solution on YOUR website!```Can you solve x in terms of y and y in terms of x for the following equation: 3y² + 4xy - 9x² = -1 Yes with the quadratic formula: To solve for y in terms of x 3y² + 4xy - 9x² = -1 Get 0 on the right 3y² + 4xy + 1 - 9x² = 0 Now we write it this way (3)y² + (4x)y + (1 - 9x²) = 0 so you can compare it with Ay² + By + C = 0 A = 3, B = 4x and C = (1 - 9x²) ___________________ -(4x) ± Ö(4x)²-4(3)(1 - 9x²) y = ------------------------------- 2(3) ________________ -4x ± Ö16x²-12(1 - 9x²) y = ------------------------------- 6 _______________ -4x ± Ö16x²-12 + 108x² y = -------------------------- 6 ________ -4x ± Ö124x²-12 y = --------------------- 6 __________ -4x ± Ö4(31x²-3) y = --------------------- 6 ______ -4x ± 2Ö31x²-3 y = ------------------ 6 ______ 2(-2x ± Ö31x²-3) y = ------------------ 6 1 ______ 2(-2x ± Ö31x²-3) y = ------------------ 6 3 ______ -2x ± Ö31x²-3) y = ------------------ 3 That's y solved in terms of x To solve for x in terms of y: 3y² + 4xy - 9x² = -1 Get 0 on the right 3y² + 4xy + 1 - 9x² = 0 Now we write it this way -9x² + 4yx + 1 + 3y² = 0 Multiply thru by -1 because it's easier when the squared term is positive: 9x² - 4yx - 1 - 3y² = 0 (9)x² + (-4y)x + (-1 - 3y²) = 0 so you can compare it with Ax² + Bx + C = 0 A = 9, B = -4y and C = (-1 - 3y²) I'll let YOU solve this, and the answer is ______ 2y ± Ö31y²+9) x = ------------------ 9 That's x solved in terms of y Edwin```