SOLUTION: Please solve the following system of equations:
x + y = -1
1/x + 1/y = 1/2
I've tried cross multiplying and all sorts to eliminate one of the unknowns, but have just mad
Algebra ->
Coordinate Systems and Linear Equations
-> Lessons
-> SOLUTION: Please solve the following system of equations:
x + y = -1
1/x + 1/y = 1/2
I've tried cross multiplying and all sorts to eliminate one of the unknowns, but have just mad
Log On
Question 15519: Please solve the following system of equations:
x + y = -1
1/x + 1/y = 1/2
I've tried cross multiplying and all sorts to eliminate one of the unknowns, but have just made things worse.
Please help. Found 2 solutions by vasu2qute, Earlsdon:Answer by vasu2qute(17) (Show Source):
You can put this solution on YOUR website! Given: x + y =-1 ----(1)
1/x+1/y=1/2 -----(2)
1/x+1/y=1/2 ===> (x+y)/xy =1/2
x+y = xy/2 (x+y=-1 according to Equation 1)
-1 = xy/2 (Substituting x+y with -1 )
xy= -2
We know that (x-y)^2 = (x+y)^2-4xy
= (-1)^2 -4(-2)
= 1 -(-8)=1+8=9
(x-y)^2 = 9
therefore x - y = 3 ------(3)
x + y = -1 ------(1)
adding (3)&(1) we get 2x = 2
x = 1
x + y = -1
1 + y = -1
y = -1 -1 = -2
therefore x=1 , y= -2
You can put this solution on YOUR website! Solve the system of equations:
1)
2) Simplify this equation.
Add the fractions of the left side. Multiply both sides by xy But so: or
Now you can solve this system of two equations:
1) and
2)
Rewrite equation 1) as:
1) and substitute into equation 2)
Now solve for y. Add 2 to both sides and simplify. Solve by factoring. Apply the zero products principle. or and/or
Now solve for x.
For y = 1, x = -y-1 = -1-1 = -2
For y = -2, x = -(-2)-1 = 2 - 1 = 1
The solutions are:
1) (-2, 1)
2) (1, -2)
Check the graph to see what this looks llike:
(
