|
Question 970923: Find the point of intersection for the three given equations. Write answer as an ordered pair.
3X^2 - 2Y^2 = 100
-4X^2 + 3Y^2 = -132
-5X^2 + 5Y^2 + 60X -20Y = 160
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 3X^2 - 2Y^2 = 100
-4X^2 + 3Y^2 = -132
-5X^2 + 5Y^2 + 60X -20Y = 160
3X^2 - 2Y^2 = 100;
-4X^2 + 3Y^2 = -132
12x^2-8y^2 = 400
-12x^2+9y^2= -396
9x^2-6y^2=300
-8x^2 +6y^2=-264
x^2=36; x=6, -6
y^2=4 ; y= 2, -2
3x^2 -8 = 100
3x^2=108 ; x= 6, -6 checks the elimination.
last equation may be rewritten
-5(x^2 -12x -y^2 + 4y = -32]
Check the four combinations of plus/minus 6,2 as an ordered pair.
(6,-2)
First yes
Second yes
Third -180 + 20 +360+40 no
(-6,2)
First yes
Second yes
Third 180 +20 -360-40 no
(6,2)
First yes
Second yes
-180 + 20 + 360-40=160
The ordered pair is (6,2)
Note, in the last equation, factoring out a -5, combining the terms and completing the square gives one an idea of what the roots might be.
|
|
|
| |
