Solve The Equation For \[$ Y \$\].$\[ Y + 6 = 20 \\]

Feb 26, 2025 by ADMIN 53 views

Introduction to Solving Linear Equations

Solving linear equations is a fundamental concept in mathematics that involves isolating the variable of interest. In this case, we are given the equation $y + 6 = 20$ and we need to solve for $y$ . This type of equation is called a linear equation because it can be graphed as a straight line on a coordinate plane.

Understanding the Equation

The given equation is $y + 6 = 20$ . To solve for $y$ , we need to isolate the variable $y$ on one side of the equation. The equation is already in a simple form, with the variable $y$ on the left-hand side and a constant term $6$ on the right-hand side.

Solving the Equation

To solve the equation, we need to get rid of the constant term $6$ that is being added to $y$ . We can do this by subtracting $6$ from both sides of the equation. This will cancel out the $6$ on the left-hand side and leave us with just $y$ .

Step-by-Step Solution

Here are the steps to solve the equation:

Subtract 6 from both sides: $y + 6 - 6 = 20 - 6$
Simplify the equation: $y = 14$

Checking the Solution

To check our solution, we can plug the value of $y$ back into the original equation and see if it is true. If we substitute $y = 14$ into the equation $y + 6 = 20$ , we get:

$14 + 6 = 20$

This is indeed true, so we can be confident that our solution is correct.

Conclusion

Solving linear equations is an important skill in mathematics that can be applied to a wide range of problems. By following the steps outlined above, we can solve equations of the form $y + c = d$ , where $c$ and $d$ are constants. In this case, we solved the equation $y + 6 = 20$ to find that $y = 14$ .

Examples of Solving Linear Equations

Here are a few more examples of solving linear equations:

$x + 3 = 12$ : To solve for $x$ , we need to subtract $3$ from both sides of the equation. This gives us $x = 9$ .
$y - 2 = 8$ : To solve for $y$ , we need to add $2$ to both sides of the equation. This gives us $y = 10$ .
$z + 4 = 15$ : To solve for $z$ , we need to subtract $4$ from both sides of the equation. This gives us $z = 11$ .

Tips for Solving Linear Equations

Here are a few tips for solving linear equations:

Make sure to isolate the variable: The goal of solving a linear equation is to isolate the variable on one side of the equation.
Use inverse operations: To solve an equation, we need to use inverse operations to get rid of the constant term.
Check your solution: Once you have solved the equation, plug the value of the variable back into the original equation to check that it is true.

Applications of Solving Linear Equations

Solving linear equations has many real-world applications, including:

Science: Linear equations are used to model the behavior of physical systems, such as the motion of objects under the influence of gravity.
Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Linear equations are used to model the behavior of economic systems, such as the supply and demand for goods and services.

Conclusion

Introduction

Solving linear equations is a fundamental concept in mathematics that involves isolating the variable of interest. In this article, we will answer some common questions about solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It can be graphed as a straight line on a coordinate plane.

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 using inverse operations, such as addition and subtraction, to get rid of the constant term.

Q: What is an inverse operation?

A: An inverse operation is an operation that undoes another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.

Q: How do I use inverse operations to solve a linear equation?

A: To use inverse operations to solve a linear equation, you need to identify the operation that is being used to add or subtract the constant term. Then, you need to use the inverse operation to get rid of the constant term.

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, while a quadratic equation is an equation in which the highest power of the variable is 2.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you need to use the quadratic formula, which is:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: What is the quadratic formula?

A: The quadratic formula is a formula that is used to solve quadratic equations. It is:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: How do I use the quadratic formula to solve a quadratic equation?

A: To use the quadratic formula to solve a quadratic equation, you need to plug in the values of a, b, and c into the formula.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is an equation in which the highest power of the variable is 1, while a system of linear equations is a set of two or more linear equations that are solved simultaneously.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, you need to use methods such as substitution and elimination to find the values of the variables.

Q: What is substitution?

A: Substitution is a method of solving a system of linear equations in which one equation is solved for one variable, and then that variable is substituted into the other equation.

Q: What is elimination?

A: Elimination is a method of solving a system of linear equations in which the equations are added or subtracted to eliminate one of the variables.

Q: How do I use substitution and elimination to solve a system of linear equations?

A: To use substitution and elimination to solve a system of linear equations, you need to identify the variables and the equations, and then use the methods of substitution and elimination to find the values of the variables.

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
Not using inverse operations
Not checking the solution
Not using the correct method for solving the equation

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, you need to plug the value of the variable back into the original equation and see if it is true.

Q: What are some real-world applications of solving linear equations?

A: Some real-world applications of solving linear equations include:

Science: Linear equations are used to model the behavior of physical systems, such as the motion of objects under the influence of gravity.
Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Linear equations are used to model the behavior of economic systems, such as the supply and demand for goods and services.

Conclusion

Solving linear equations is an important skill in mathematics that can be applied to a wide range of problems. By following the steps outlined above, we can solve equations of the form $y + c = d$ , where $c$ and $d$ are constants. In this article, we have answered some common questions about solving linear equations, including how to use inverse operations, substitution, and elimination to solve equations.