Solving Equations Involving Variables: A Step-by-Step Guide

In this guide, we will walk through the process of finding the value of a variable in a given algebraic equation. Specifically, we will solve for the variable z in the equation 5x 2y - 3z 16, given that x 2 and y 3. Let's break down the process step-by-step and explore each method in more detail.

Method 1: Direct Substitution

Given:

5x 2y - 3z 16

x 2

y 3

Step 1: Substitute the values of x and y into the equation.

5(2) 2(3) - 3z 16

Step 2: Calculate the constants.

10 6 - 3z 16

Step 3: Combine the constants on the left side of the equation.

16 - 3z 16

Step 4: Subtract 16 from both sides of the equation.

-3z 0

Step 5: Divide both sides by -3.

z 0

The value of z is 0.

Method 2: Isolating z with a Modified Equation

Given:

5x 2y - 3z 16

We start by isolating the term containing z.

-3z 16 - 5x - 2y

Step 1: Substitute x 2 and y 3.

-3z 16 - 5(2) - 2(3)

Step 2: Calculate the constants.

-3z 16 - 10 - 6

Step 3: Combine the constants on the right side of the equation.

-3z 0

Step 4: Divide both sides by -3.

z 0

The value of z is 0.

Conclusion

In both methods, we arrive at the same conclusion that the value of the variable z is 0. This demonstrates the consistency of algebraic manipulation and the importance of careful calculation in solving equations.

Keywords: Variable substitution, algebraic equations, equation solving

Additional Reading:

Introduction to Algebraic Equations Understanding Variable Substitution Basic Algebraic Operations