Explanation:
To solve the given system of equations:
1. x(y+z) = 44
2. y(z+x) = 50
3. z(x+y) = 54
We can use substitution or elimination method. Let's use the substitution method.
From equation 1, we have y + z = 44/x.
Rearranging equation 2 gives us y = 50/(z+x), and equation 3 gives us z = 54/(x+y).
Now, substitute these expressions for y and z in equation 1:
(y + z) = 44/x
(50/(z+x)) + (54/(x+y)) = 44/x
To simplify, let's cross-multiply:
50(x+y) + 54(z+x) = 44(z+x)
Expanding both sides:
50x + 50y + 54z + 54x = 44z + 44x
Collecting like terms:
50x + 54x - 44x + 50y + 54z = 44z
Now, simplify further:
60x + 50y + 10z = 44z
Rearranging terms:
60x + 50y = 34z
Divide both sides by 2:
30x + 25y = 17z
Now, we have three equations:
1. y + z = 44/x
2. 30x + 25y = 17z
3. z = 54/(x+y)
To find the values of x, y, and z, we need further information or equations. The given system is not sufficient to solve for the values of x, y, and z.