Substitute The Value Of $y$.$\[ \begin{array}{l} x = 3 - 2y \\ x = 3 - 2(?) \end{array} \\]

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Introduction

In algebra, solving for a variable in a linear equation is a fundamental concept. It involves isolating the variable on one side of the equation, while the constant terms are on the other side. In this article, we will focus on solving for $y$ in a linear equation, specifically in the equation $x = 3 - 2y$. We will use step-by-step instructions and provide examples to illustrate the process.

Understanding the Equation

The given equation is $x = 3 - 2y$. To solve for $y$, we need to isolate $y$ on one side of the equation. The equation is already in the form of $x = f(y)$, where $f(y)$ is a function of $y$. Our goal is to rewrite the equation in the form of $y = f(x)$.

Step 1: Add $2y$ to Both Sides

To isolate $y$, we need to get rid of the $-2y$ term on the right-hand side of the equation. We can do this by adding $2y$ to both sides of the equation. This will result in:

$x + 2y = 3$

Step 2: Subtract $x$ from Both Sides

Next, we need to get rid of the $x$ term on the left-hand side of the equation. We can do this by subtracting $x$ from both sides of the equation. This will result in:

$2y = 3 - x$

Step 3: Divide Both Sides by 2

Finally, we need to isolate $y$ by dividing both sides of the equation by 2. This will result in:

$y = \frac{3 - x}{2}$

Conclusion

In this article, we have solved for $y$ in the linear equation $x = 3 - 2y$. We used step-by-step instructions and provided examples to illustrate the process. By following these steps, we were able to isolate $y$ and rewrite the equation in the form of $y = f(x)$.

Example 1: Solving for $y$

Suppose we have the equation $x = 3 - 2y$, and we want to solve for $y$ when $x = 2$. We can substitute $x = 2$ into the equation and solve for $y$.

$2 = 3 - 2y$

Adding $2y$ to both sides, we get:

$2 + 2y = 3$

Subtracting 2 from both sides, we get:

$2y = 1$

Dividing both sides by 2, we get:

$y = \frac{1}{2}$

Example 2: Solving for $y$

Suppose we have the equation $x = 3 - 2y$, and we want to solve for $y$ when $x = 5$. We can substitute $x = 5$ into the equation and solve for $y$.

$5 = 3 - 2y$

Adding $2y$ to both sides, we get:

$5 + 2y = 3$

Subtracting 5 from both sides, we get:

$2y = -2$

Dividing both sides by 2, we get:

$y = -1$

Tips and Tricks

• When solving for $y$, make sure to isolate $y$ on one side of the equation.
• Use the correct order of operations when simplifying the equation.
• Check your work by plugging the solution back into the original equation.

Common Mistakes

• Failing to isolate $y$ on one side of the equation.
• Not using the correct order of operations when simplifying the equation.
• Not checking the solution by plugging it back into the original equation.

Conclusion

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Introduction

In our previous article, we discussed how to solve for $y$ in a linear equation. We provided step-by-step instructions and examples to illustrate the process. In this article, we will answer some frequently asked questions about solving for $y$ in a linear equation.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $y$) is 1. Linear equations can be written in the form of $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: How do I know if an equation is linear?

A: To determine if an equation is linear, look for the following characteristics:

• The highest power of the variable is 1.
• The equation can be written in the form of $y = mx + b$.
• The equation has a constant term (the y-intercept).

Q: What is the difference between solving for $y$ and solving for $x$?

A: Solving for $y$ involves isolating $y$ on one side of the equation, while solving for $x$ involves isolating $x$ on one side of the equation. In other words, when solving for $y$, you are finding the value of $y$ that makes the equation true, while when solving for $x$, you are finding the value of $x$ that makes the equation true.

Q: Can I use the same steps to solve for $x$ as I do to solve for $y$?

A: Yes, you can use the same steps to solve for $x$ as you do to solve for $y$. The only difference is that you will be isolating $x$ on one side of the equation instead of $y$.

Q: What if I have a quadratic equation? Can I still solve for $y$?

A: Quadratic equations are equations in which the highest power of the variable is 2. While you can still solve for $y$ in a quadratic equation, the process is more complex and may involve using the quadratic formula.

Q: Can I use a calculator to solve for $y$?

A: Yes, you can use a calculator to solve for $y$. However, it's always a good idea to check your work by plugging the solution back into the original equation.

Q: What if I make a mistake when solving for $y$?

A: If you make a mistake when solving for $y$, don't worry! Just go back and recheck your work. Make sure to follow the steps carefully and double-check your calculations.

Q: Can I solve for $y$ in an equation with multiple variables?

A: Yes, you can solve for $y$ in an equation with multiple variables. However, the process may be more complex and may involve using substitution or elimination methods.

Conclusion

Solving for $y$ in a linear equation is a fundamental concept in algebra. By following the steps outlined in this article and answering some frequently asked questions, you can become more confident in your ability to solve for $y$ in a linear equation.

Tips and Tricks

• Make sure to isolate $y$ on one side of the equation.
• Use the correct order of operations when simplifying the equation.
• Check your work by plugging the solution back into the original equation.
• Use a calculator to check your work, but make sure to double-check your calculations.

Common Mistakes

• Failing to isolate $y$ on one side of the equation.
• Not using the correct order of operations when simplifying the equation.
• Not checking the solution by plugging it back into the original equation.

Conclusion

Solving for $y$ in a linear equation is a fundamental concept in algebra. By following the steps outlined in this article and answering some frequently asked questions, you can become more confident in your ability to solve for $y$ in a linear equation. Remember to isolate $y$ on one side of the equation, use the correct order of operations, and check your work by plugging the solution back into the original equation.