# Help solving difficult simultaneous quadratic equation

• Jun 4th 2012, 06:30 AM
markling
Help solving difficult simultaneous quadratic equation
I'm stuck on a problem in an exercise book. It gives the answer, but I just can't get the same answer. Here's the problem:

Find the co-ordinates of the point of intersection of the given straight line and curve:

i. 2x - 5y =6
ii. 2xy - 4x² - 3y = 1

Following an example earlier in the book, I went this way:

i. 2x = 6 + 5y
i. 4x² = (6 + 5y)² = (6 + 5y)(6 + 5y) = 36 + 60y + 25y²

i into ii:

ii. y(6 + 5y) -(36 + 60y + 25y²) - 3y = 1
ii. 6y + 5y² -36 - 60y - 25y² -3y = 1
ii. -20y² - 57y - 37 = 0

When I put that last line into the quadratic formula, I only get one root. The given answer has two. I'm clearly doing something wrong. Would someone please help?
• Jun 4th 2012, 06:56 AM
earboth
Re: Help solving difficult simultaneous quadratic equation
Quote:

Originally Posted by markling
I'm stuck on a problem in an exercise book. It gives the answer, but I just can't get the same answer. Here's the problem:

Find the co-ordinates of the point of intersection of the given straight line and curve:

i. 2x - 5y =6
ii. 2xy - 4x² - 3y = 1

Following an example earlier in the book, I went this way:

i. 2x = 6 + 5y
i. 4x² = (6 + 5y)² = (6 + 5y)(6 + 5y) = 36 + 60y + 25y²

i into ii:

ii. y(6 + 5y) -(36 + 60y + 25y²) - 3y = 1
ii. 6y + 5y² -36 - 60y - 25y² -3y = 1
ii. -20y² - 57y - 37 = 0

When I put that last line into the quadratic formula, I only get one root. <--- I get: y=-1 or $y = -\frac{37}{20}$ !
... and consequently $x = \frac12~\vee~x=-\frac{13}8$