Make { Y $}$ The Subject:${ 2yz + 4x = ? }$Where { Z = 15 $}$ And { X = 3 $}$.
Introduction
In algebra, solving for the subject in a linear equation is a fundamental concept that involves isolating the variable of interest on one side of the equation. This is a crucial skill in mathematics, as it allows us to find the value of a variable when given a specific equation. In this article, we will explore how to solve for the subject in a linear equation, using a specific example to illustrate the process.
The Equation
The given equation is:
2yz + 4x = ?
We are also given the values of z and x, which are:
z = 15 x = 3
Step 1: Substitute the Given Values
To solve for the subject, we need to substitute the given values of z and x into the equation. This will give us:
2(15)y + 4(3) = ?
Step 2: Simplify the Equation
Next, we need to simplify the equation by multiplying the numbers outside the parentheses with the numbers inside. This will give us:
30y + 12 = ?
Step 3: Isolate the Variable
Now, we need to isolate the variable y by getting rid of the constant term on the same side of the equation. We can do this by subtracting 12 from both sides of the equation. This will give us:
30y = -12
Step 4: Solve for the Variable
Finally, we need to solve for the variable y by dividing both sides of the equation by 30. This will give us:
y = -12/30
Step 5: Simplify the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 6. This will give us:
y = -2/5
Conclusion
In this article, we have shown how to solve for the subject in a linear equation using a specific example. We have substituted the given values into the equation, simplified the equation, isolated the variable, and solved for the variable. The final answer is y = -2/5.
Example Use Cases
Solving for the subject in a linear equation has many practical applications in mathematics and real-life situations. Here are a few examples:
- Physics: In physics, solving for the subject in a linear equation can help us find the velocity of an object given its acceleration and time.
- Engineering: In engineering, solving for the subject in a linear equation can help us find the stress on a material given its Young's modulus and strain.
- Economics: In economics, solving for the subject in a linear equation can help us find the demand for a product given its price and income.
Tips and Tricks
Here are a few tips and tricks to help you solve for the subject in a linear equation:
- Use the order of operations: When simplifying the equation, make sure to follow the order of operations (PEMDAS).
- Isolate the variable: To isolate the variable, get rid of the constant term on the same side of the equation.
- Simplify fractions: To simplify fractions, divide both the numerator and the denominator by their greatest common divisor.
Conclusion
Q: What is the subject in a linear equation?
A: The subject in a linear equation is the variable that we are trying to solve for. In the equation 2yz + 4x = ?, the subject is y.
Q: How do I know which variable to solve for?
A: To determine which variable to solve for, look at the equation and identify the variable that is being isolated on one side of the equation. In the equation 2yz + 4x = ?, we are trying to solve for y.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation in which the highest power of the variable is 1. For example, 2yz + 4x = ? is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, 2yz^2 + 4x = ? is a quadratic equation.
Q: How do I solve a linear equation with multiple variables?
A: To solve a linear equation with multiple variables, follow the same steps as solving a linear equation with one variable. Substitute the given values into the equation, simplify the equation, isolate the variable, and solve for the variable.
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when simplifying an equation. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I simplify a fraction?
A: To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify the fraction 12/30, divide both the numerator and the denominator by 6 to get 2/5.
Q: What is the greatest common divisor (GCD)?
A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 12 and 30 is 6.
Q: How do I isolate a variable?
A: To isolate a variable, get rid of the constant term on the same side of the equation. For example, in the equation 2yz + 4x = ?, we can isolate y by subtracting 4x from both sides of the equation to get 2yz = -4x.
Q: What is the final answer to the equation 2yz + 4x = ?
A: The final answer to the equation 2yz + 4x = ? is y = -2/5, given that z = 15 and x = 3.
Conclusion
In this article, we have answered some frequently asked questions about solving for the subject in a linear equation. We have covered topics such as the definition of a linear equation, the order of operations, simplifying fractions, and isolating variables. By following the steps outlined in this article, you can become proficient in solving for the subject in a linear equation.