Complete The Missing Value In The Solution To The Equation:$-4x - Y = 24$( $\square$ , 8)Complete The Missing Value For The X-coordinate In The Solution.

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 linear equations in two variables, with a specific emphasis on completing the missing value in the solution. We will use the equation $-4x - y = 24$ as a case study to illustrate the steps involved in solving linear equations.

Understanding the Equation

The given equation is $-4x - y = 24$. This is a linear equation in two variables, $x$ and $y$. The equation is in the form of $ax + by = c$, where $a$, $b$, and $c$ are constants. In this case, $a = -4$, $b = -1$, and $c = 24$.

The Solution to the Equation

The solution to the equation $-4x - y = 24$ is given as $(\square, 8)$. This means that the value of $x$ is missing, and we need to find it. To do this, we can use the method of substitution or elimination.

Method of Substitution

One way to solve the equation is by using the method of substitution. We can start by isolating one of the variables, say $y$. We can do this by adding $4x$ to both sides of the equation:

$$-y = 24 + 4x$$

Next, we can multiply both sides of the equation by $-1$ to get:

$$y = -24 - 4x$$

Now, we can substitute this expression for $y$ into the original equation:

$$-4x - (-24 - 4x) = 24$$

Simplifying the equation, we get:

$$-4x + 24 + 4x = 24$$

Combine like terms:

$$24 = 24$$

This is a true statement, which means that the equation is an identity. However, this does not help us find the value of $x$.

Method of Elimination

Another way to solve the equation is by using the method of elimination. We can start by multiplying both sides of the equation by $-1$ to get:

$$4x + y = -24$$

Now, we can add this equation to the original equation:

$$-4x - y = 24$$

$$4x + y = -24$$

Combine like terms:

$$0 = -48$$

This is a false statement, which means that the two equations are inconsistent. However, this does not help us find the value of $x$.

Using the Given Solution

Since we are given the solution $(\square, 8)$, we can use it to find the value of $x$. We can substitute $y = 8$ into the original equation:

$$-4x - 8 = 24$$

Add $8$ to both sides of the equation:

$$-4x = 32$$

Divide both sides of the equation by $-4$:

$$x = -8$$

Therefore, the value of $x$ is $-8$.

Conclusion

In this article, we have solved the linear equation $-4x - y = 24$ using the method of substitution and elimination. We have also used the given solution $(\square, 8)$ to find the value of $x$. The value of $x$ is $-8$, which means that the solution to the equation is $(-8, 8)$.

Frequently Asked Questions

• What is the solution to the equation $-4x - y = 24$?
• How do I solve linear equations in two variables?
• What is the method of substitution?
• What is the method of elimination?

Final Answer

The final answer is $\boxed{-8}$.

Introduction

In our previous article, we solved the linear equation $-4x - y = 24$ using the method of substitution and elimination. We also used the given solution $(\square, 8)$ to find the value of $x$. In this article, we will answer some frequently asked questions related to solving linear equations.

Q&A

Q1: What is the solution to the equation $-4x - y = 24$?

A1: The solution to the equation $-4x - y = 24$ is $(-8, 8)$.

Q2: How do I solve linear equations in two variables?

A2: To solve linear equations in two variables, you can use the method of substitution or elimination. The method of substitution involves isolating one of the variables and substituting it into the other equation. The method of elimination involves adding or subtracting the two equations to eliminate one of the variables.

Q3: What is the method of substitution?

A3: The method of substitution involves isolating one of the variables and substituting it into the other equation. For example, if we have the equation $-4x - y = 24$ and we want to isolate $y$, we can add $4x$ to both sides of the equation to get $y = -24 - 4x$.

Q4: What is the method of elimination?

A4: The method of elimination involves adding or subtracting the two equations to eliminate one of the variables. For example, if we have the equation $-4x - y = 24$ and we want to eliminate $y$, we can add the equation $4x + y = -24$ to get $0 = -48$, which is a false statement.

Q5: How do I know if the two equations are consistent or inconsistent?

A5: If the two equations are consistent, they will have a solution. If the two equations are inconsistent, they will not have a solution. To determine if the two equations are consistent or inconsistent, you can use the method of substitution or elimination.

Q6: What is the difference between a consistent and an inconsistent system of equations?

A6: A consistent system of equations is one that has a solution. An inconsistent system of equations is one that does not have a solution.

Q7: How do I find the value of $x$ in a linear equation?

A7: To find the value of $x$ in a linear equation, you can use the method of substitution or elimination. You can also use the given solution to find the value of $x$.

Q8: What is the final answer to the equation $-4x - y = 24$?

A8: The final answer to the equation $-4x - y = 24$ is $\boxed{-8}$.

Conclusion

In this article, we have answered some frequently asked questions related to solving linear equations. We have also provided examples and explanations to help you understand the concepts. If you have any more questions, feel free to ask.

Frequently Asked Questions

• What is the solution to the equation $-4x - y = 24$?
• How do I solve linear equations in two variables?
• What is the method of substitution?
• What is the method of elimination?
• How do I know if the two equations are consistent or inconsistent?
• What is the difference between a consistent and an inconsistent system of equations?
• How do I find the value of $x$ in a linear equation?
• What is the final answer to the equation $-4x - y = 24$?

Final Answer

The final answer is $\boxed{-8}$.