Solving for Y in the Equation 2x - y 7 with x 2: A Guide to Linear Equations

In this article, we will walk through the process of solving for Y in the linear equation 2x - y 7, given the value of x 2. This guide is designed to help you understand the substitution method and how it can be applied to solve problems involving linear equations.

Introduction to Linear Equations

A linear equation is an equation that forms a straight line when graphed. The general form of a linear equation is ax by c, where a, b, and c are constants, and a and b are not both zero. In our specific example, the equation is 2x - y 7, which is already in the standard form.

Solving for Y: The Substitution Method

The substitution method is a common technique used in algebra to solve systems of equations. Here, we will use this method to find the value of Y given that x 2.

Given:

2x - y 7 x 2

Steps to Solve:

Substitute the given value of x into the equation 2x - y 7. Simplify the equation to isolate y. Solve for y.

Step 1: Substitute the Value of x

Given x 2:

[ 2(2) - y 7 ]

Step 2: Simplify the Equation

Perform the multiplication:

[ 4 - y 7 ]

Step 3: Solve for y

To isolate y, subtract 4 from both sides of the equation:

[ - y 7 - 4 ] [ - y 3 ]

Multiply both sides by -1 to solve for y:

[ y -3 ]

Therefore, the value of y is -3.

Alternative Methods and Solutions

There are other methods to solve for y, such as the graphing method and the elimination method. However, for this particular linear equation, the substitution method is the most straightforward and efficient approach.

Conclusion

Understanding how to solve for y in a linear equation is crucial for many mathematical and real-world applications. By following the steps explained in this guide, you can solve for y when given an equation and a specific value for x.

Related Keywords:

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