We can find the value of x by dividing equation 2 by equation 3:
$\frac{yz}{zx} = \frac{35}{21}$
$\frac{y}{z} = \frac{5}{3}$
Multiplying this equation by equation 1 gives us:
$\frac{y}{z} \cdot xy = \frac{5}{3} \cdot 15$
$y^2 = 25$
$y = 5$
Substituting this value of y into equation 2 gives us:
$z \cdot 5 = 35$
$z = 7$
And substituting this value of z into equation 1 gives us:
$x \cdot 5 \cdot 7 = 15$
$x = \frac{3}{7}$
The sum of the positive valued solutions is $5 + 7 + \frac{3}{7} = \boxed{\frac{119}{7}}$.
Determine the sum of the positive valued solution to the simultaneous equations:
xy=15, yz=35,zx=21
1 answer