Solve this System of Equations: .5= (x-40)/(x-y) and .5=(40-y)/(x-y)

[bmed90]

Homework Statement

Solve for x and y

.5= (x-40)/(x-y) and .5=(40-y)/(x-y)

Homework Equations

The Attempt at a Solution

I have been trying to solve this system of equations for hours and I can't seem to get it. Can anyone please give it a shot and see what they get? I'm sure I am overlooking a simple mistake. Thanks

 

[QuarkCharmer]

.5= (x-40)/(x-y) and .5=(40-y)/(x-y)

You need to first isolate a single variable for the substitution method, or put the equations in the standard form for elimination. I chose to use the substitution method (and what better variable to chose then Y to double check with a calc). I will show you my work for the first equation.

.5 = (x-40)/(x-y)

//Multiply both sides of the left eq. by the denominator of the right to cancel the denominators/fractions.
.5(x-y) = (x-40)

//Distribute out the .5(x-y)
.5x-.5y = x-40

//Subtract a .5x from both sides
-.5y = .5x - 40

//Finally divide both sides by a -.5 to isolate the variable y, resulting in:

y = (.5x-40)/(-.5)

Here is what I got for the two in terms of Y.

Y1= (.5x-40)/(-.5)

Y2= (40+.5x)/(.5)

Surely you know where to go from here? (Substitution, Elimination, Matrice, or a graphing calculator etc)

How do your steps look? Perhaps if you show your steps up until, and after this point we can figure out where you are going wrong.

Cheers

 

[HallsofIvy]

Personally, I would get rid of all fractions by multiplying each equation by 2(x- y).

That gives x- y= 2(x- 40) and x- y= 2(40- y). Multiplying those out, x- y= 2x- 80 or x+ y= 80, and x- y= 80- 2y or x+ y= 80. Those two equations are the same so the original equations were not "independent". There are an infinite number of solutions. Given any x, (x, y)= (x, 80- x) is a solution (except (40, 40) for which x- y= 0 and the original equation makes no sense).

 

[zgozvrm]

Personally, I would get rid of all fractions by multiplying each equation by 2(x- y).

That gives x- y= 2(x- 40) and x- y= 2(40- y). Multiplying those out, x- y= 2x- 80 or x+ y= 80, and x- y= 80- 2y or x+ y= 80. Those two equations are the same so the original equations were not "independent". There are an infinite number of solutions. Given any x, (x, y)= (x, 80- x) is a solution (except (40, 40) for which x- y= 0 and the original equation makes no sense).

Again with giving out the answer! I thought that wasn't allowed in the homework forum!