Question

2x = 5 y
and 15 y =z
find relation between X and Z ​

Answer 1

Answer:

A SOLUTION:

Typically we need a system of three equations to solve a system with three variables.

We can use the ratios between x, y, and z to construct additional equations.

First, we separate the three-part proportion into two-part proportions.

x : y : z = 4 : -2 : 5

If we write the ratios that tell us about x, we can use substitution to find x, y, and z.

We can say that

x : y = 4 : -2.

Translate the proportion into a fraction and solve for y.

x/y=4/-2

-2x=4y

y=(-1/2)x

Using similar reasoning, the relationship between x and z is

x : z = 4 : 5

x/z = 4/5

5x = 4z

z = (5/4)x

Now substitute (-1/2)x for y and (5/4)x for z in the equation x + 3y + z = 15.

x + 3((-1/2)x) + ((5/4)x) = 15

x - (3/2)x + (5/4)x = 15

Multiply every term by 4 to clear the denominators.

4x - 6x + 5x = 60

3x = 60

x = 20

Use the proportions to find y and z.

y = (-1/2)x

y = (-1/2)(20)

y = -10

z = (5/4)x

z = (5/4)(20)

z = 25

We have x=20, y=-10, and z=25.

Verify these values in the equation and ratios.

x + 3y + z = 15

(20) + 3(-10) + 25 = 15

20 - 30 + 25 = 15

15 = 15

CHECK!

x : y : z = 4 : -2 : 5

(20) : (-10) : (25) = 4: -2 : 5

Since we can multiply the numbers on the left by a favor of 1/5 to get the corresponding numbers on the right, this proportion is true. CHECK!

Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Answer 2

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2x = 5y

x=5y/2

15 y = z

y = z/15

x=5×z/15×2

x=z/6

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