Solve z from the following equations: xy=12; yz=20; zx=15

Given the system of equations:

\[
xy = 12
\]
\[
yz = 20
\]
\[
zx = 15
\]

We want to find the value of \( z \).

### Step 1: Multiply all three equations together.

\[
(xy) \cdot (yz) \cdot (zx) = 12 \cdot 20 \cdot 15
\]

This can be written as:

\[
(xyz)^2 = 12 \cdot 20 \cdot 15
\]

### Step 2: Calculate the right-hand side.

\[
12 \times 20 = 240
\]
\[
240 \times 15 = 3600
\]

Thus:

\[
(xyz)^2 = 3600
\]

### Step 3: Take the square root of both sides.

\[
xyz = \sqrt{3600} = 60
\]

### Step 4: Solve for \( z \).

Using the equation \( xyz = 60 \), we can solve for \( z \) using any of the original equations. Let's use the first equation \( xy = 12 \):

\[
z = \frac{xyz}{xy} = \frac{60}{12} = 5
\]

So, the value of \( z \) is \( \boxed{5} \).

Would you like further details or have any questions? Here are five additional questions that relate to this problem:

1. How would you solve for \( x \) and \( y \) in the system of equations?
2. What is the significance of multiplying all three equations together?
3. How would you check if the calculated value of \( z \) is correct?
4. Can this method be generalized to solve other similar systems of equations?
5. What are some common mistakes to avoid when solving systems of equations like this?

**Tip:** Always verify your solution by substituting it back into the original equations.

Learn how to solve for z in the system of equations xy = 12, yz = 20, zx = 15 with a step-by-step solution. This problem involves understanding systems of equations and using multiplication of equations to find the solution. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation