Solve for x and y
40 / (x+y) = 2.70
40 / (x-y) = 4.70
To solve for x and y in the given equations, we'll begin by isolating x in both equations and then solving for y.
Equation 1: 40 / (x+y) = 2.70
To isolate x, we'll start by multiplying both sides of the equation by (x+y):
40 = 2.70 * (x+y)
Divide both sides of the equation by 2.70:
40 / 2.70 = x + y
Now we have the equation:
14.81 = x + y ----(Equation A)
Equation 2: 40 / (x-y) = 4.70
To isolate x, we'll start by multiplying both sides of the equation by (x-y):
40 = 4.70 * (x-y)
Divide both sides of the equation by 4.70:
40 / 4.70 = x - y
Now we have the equation:
8.51 = x - y ----(Equation B)
Now, we have a system of two equations with two variables (x and y).
We'll solve this system of equations by eliminating one variable. Let's eliminate y.
Add Equation A and Equation B:
14.81 + 8.51 = (x + y) + (x - y)
Simplifying both sides of the equation:
23.32 = 2x
Divide both sides of the equation by 2:
23.32 / 2 = x
Solving for x:
x = 11.66
Now substitute the value of x into either Equation A or Equation B. Let's use Equation A:
14.81 = 11.66 + y
Subtract 11.66 from both sides of the equation:
14.81 - 11.66 = y
Solving for y:
y = 3.15
Therefore, the solution to the given system of equations is:
x = 11.66
y = 3.15