Which Value Of $y$ Makes The Equation $13 - Y = 17$ True?A) \$y = -13$[/tex\]B) $y = -4$C) $y = 4$D) \$y = 13$[/tex\]
Introduction
Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a simple linear equation, $13 - y = 17$, and determine the value of $y$ that makes the equation true.
Understanding Linear Equations
A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.
Solving the Equation
To solve the equation $13 - y = 17$, we need to isolate the variable $y$. We can start by adding $y$ to both sides of the equation, which gives us:
This simplifies to:
Next, we can subtract 17 from both sides of the equation, which gives us:
This simplifies to:
Therefore, the value of $y$ that makes the equation $13 - y = 17$ true is $y = -4$.
Checking the Answer
To verify our answer, we can plug $y = -4$ back into the original equation:
This simplifies to:
Which is true. Therefore, our answer is correct.
Conclusion
Solving linear equations is an essential skill for students to master. By following the steps outlined in this article, we can solve simple linear equations like $13 - y = 17$ and determine the value of the variable. In this case, the value of $y$ that makes the equation true is $y = -4$.
Common Mistakes to Avoid
When solving linear equations, there are several common mistakes to avoid. These include:
- Not isolating the variable: Make sure to isolate the variable on one side of the equation.
- Not checking the answer: Always plug the answer back into the original equation to verify that it is true.
- Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying the equation.
Practice Problems
To practice solving linear equations, try the following problems:
Real-World Applications
Linear equations have many real-world applications, including:
- Finance: Linear equations are used to calculate interest rates, investment returns, and other financial metrics.
- Science: Linear equations are used to model population growth, chemical reactions, and other scientific phenomena.
- Engineering: Linear equations are used to design and optimize systems, including electrical circuits, mechanical systems, and computer networks.
Conclusion
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.
Q: How do I solve a linear equation?
A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
Q: What is the order of operations?
A: The order of operations is a set of rules that tells you 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 check my answer?
A: To check your answer, plug the value of the variable back into the original equation and simplify. If the equation is true, then your answer is correct.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not isolating the variable: Make sure to isolate the variable on one side of the equation.
- Not checking the answer: Always plug the answer back into the original equation to verify that it is true.
- Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying the equation.
Q: Can I use a calculator to solve linear equations?
A: Yes, you can use a calculator to solve linear equations. However, make sure to follow the order of operations and check your answer to ensure that it is correct.
Q: How do I solve a linear equation with fractions?
A: To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.
Q: Can I solve a linear equation with decimals?
A: Yes, you can solve a linear equation with decimals. However, make sure to follow the order of operations and check your answer to ensure that it is correct.
Q: How do I solve a linear equation with variables on both sides?
A: To solve a linear equation with variables on both sides, you need to add or subtract the same value to both sides of the equation to eliminate the variable on one side.
Q: Can I solve a linear equation with absolute values?
A: Yes, you can solve a linear equation with absolute values. However, make sure to follow the order of operations and check your answer to ensure that it is correct.
Conclusion
In conclusion, solving linear equations is an essential skill for students to master. By following the steps outlined in this article, you can solve simple linear equations and determine the value of the variable. Remember to always check your answer and follow the order of operations to ensure that your solution is correct. With practice and patience, you can become proficient in solving linear equations and apply them to real-world problems.