SOLUTION: Solve the simultaneous equation:
4x² - 9y² = 19
2x + 3y = 1
Algebra.Com
Question 1142955: Solve the simultaneous equation:
4x² - 9y² = 19
2x + 3y = 1
Found 2 solutions by rothauserc, greenestamps:
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The line 2x +3y = 1 is tangent to 4x^2 -9y^2 = 19
:
Solve the linear equation for y
:
1) y = -2x/3 +1/3
:
substitute for y in the equation of the hyperbole
:
4x^2 -9(-2x/3 +1/3)^2 = 19
:
4x^2 -9(4x^2/9 -4x/9 +1/9) = 19
:
4x^2 -4x^2 +4x -1 = 19
:
4x -20 = 0
:
4x = 20
:
x = 5
:
use equation 1 to get the value of y
:
y = -2(5)/3 +1/3 = -3
:
******************************************************************
solution is x = 5, y = -3 which is the point (5, -3)
:
check the solution
:
hyperbole
:
4(5^2) -9(-3)^2 = 19
:
100 -81 = 19
:
19 = 19
:
Line
:
2(5) +3(-3) = 1
:
10 -9 = 1
:
1 = 1
:
answers check
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Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
(1)
(2)
Rewrite (1) by factoring the left had side:
(3)
Use (2) and (3) to conclude that
(4)
Add (2) and (4):
(5)
Substitute (5) in (2):
ANSWER: (x,y) = (5,-3)
CHECK:
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