Resolving the Equations: Finding the Value of x with y z2 and x y - 2

When dealing with algebraic equations, solving for a specific variable often involves substituting one equation into another. In this article, we will walk through a step-by-step process to find the value of x given the equations x y - 2 and y z2, where z is a constant. Let's explore the solution process and understand each step thoroughly.

Step-by-Step Guide to Solve for x

Given the equations:

x y - 2 y z2 z 0

Let's substitute these values into the equations to find the value of x.

Step 1: Understanding the Given Values

The value of z is given as 0. Therefore:

z  0

Step 2: Substituting z into the Equation for y

According to the second equation, y is defined as z squared:

y  z2

Since z 0, replace z with 0:

y  02y  0

Therefore, the value of y is 0.

Step 3: Substituting y into the Equation for x

Now, substitute the value of y into the first equation:

x  y - 2

Since y 0, replace y with 0:

x  0 - 2x  -2

Thus, the value of x is -2.

Step 4: Conclusion

By following the steps of algebraic substitution, we have determined that when z 0, y 02 0, and x 0 - 2 -2.

In summary, the value of x is -2 given the provided equations.

Frequently Asked Questions

Q: Why is it important to substitute values step-by-step in algebraic equations?
A: Substituting values step-by-step ensures accuracy and helps avoid missing any crucial steps in the solution process. Each substitution builds on the previous one, leading to a clear and understandable final result. Q: Can the value of x change if z has a different value?
A: Yes, the value of x can change if z takes a different value. Each step in the equation depends on the values of the variables defined in the equations. By changing the value of z, the values of y and x will also change accordingly. Q: How can I verify whether my solution for x is correct?
A: You can verify your solution by plugging the values of y and z back into the original equations. If the equations hold true with the substituted values, your solution is correct.

Conclusion

Understanding and solving algebraic equations step-by-step is a fundamental skill in mathematics. By following the process of substituting values and verifying the results, you can gain confidence in solving more complex equations and problems in the future. Remember, each step matters!