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
