Malik's Solution To The Equation $\frac{2}{5} X - 4 Y = 10$, When $x = 60$, Is Shown Below:$\[ \begin{array}{l} \frac{2}{5} X - 4 Y = 10 \\ \frac{2}{5} (60) - 4 Y = 10 \\ \frac{120}{5} - 4 Y = 10 \\ 24 - 4 Y = 10 \\ 24 - 4 Y + 4 Y

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 explore how to solve linear equations, using the example of Malik's solution to the equation $\frac{2}{5} x - 4 y = 10$, when $x = 60$. We will break down the solution step by step, explaining each step in detail.

Understanding Linear Equations

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form $ax + by = c$, where $a$, $b$, and $c$ are constants, and $x$ and $y$ are variables. Linear equations can be solved using various methods, including substitution, elimination, and graphing.

Malik's Solution

Malik's solution to the equation $\frac{2}{5} x - 4 y = 10$, when $x = 60$, is shown below:

$${ \begin{array}{l} \frac{2}{5} x - 4 y = 10 \\ \frac{2}{5} (60) - 4 y = 10 \\ \frac{120}{5} - 4 y = 10 \\ 24 - 4 y = 10 \\ 24 - 4 y + 4 y \end{array} }$$

Step 1: Substitute the Value of $x$

The first step in Malik's solution is to substitute the value of $x$ into the equation. In this case, $x = 60$. So, we substitute $60$ for $x$ in the equation:

$${ \frac{2}{5} x - 4 y = 10 }$$

becomes

$${ \frac{2}{5} (60) - 4 y = 10 }$$

Step 2: Simplify the Equation

The next step is to simplify the equation by evaluating the expression $\frac{2}{5} (60)$. This is equal to $\frac{120}{5}$, which simplifies to $24$.

$${ \frac{120}{5} - 4 y = 10 }$$

becomes

$${ 24 - 4 y = 10 }$$

Step 3: Isolate the Variable $y$

The final step is to isolate the variable $y$ by adding $4y$ to both sides of the equation. This gives us:

$${ 24 - 4 y + 4 y = 10 + 4 y }$$

which simplifies to

$${ 24 = 10 + 4 y }$$

Solving for $y$

To solve for $y$, we need to isolate $y$ on one side of the equation. We can do this by subtracting $10$ from both sides of the equation:

$${ 24 - 10 = 4 y }$$

which simplifies to

$${ 14 = 4 y }$$

Final Step: Divide by 4

The final step is to divide both sides of the equation by $4$ to solve for $y$:

$${ \frac{14}{4} = y }$$

which simplifies to

$${ y = \frac{7}{2} }$$

Conclusion

In this article, we have explored how to solve linear equations using the example of Malik's solution to the equation $\frac{2}{5} x - 4 y = 10$, when $x = 60$. We have broken down the solution step by step, explaining each step in detail. We have shown how to substitute the value of $x$, simplify the equation, isolate the variable $y$, and finally solve for $y$. This is a crucial skill for students to master, and we hope that this article has provided a clear and concise guide to solving linear equations.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid. These include:

• Not substituting the value of $x$: Make sure to substitute the value of $x$ into the equation before simplifying.
• Not simplifying the equation: Make sure to simplify the equation by evaluating any expressions and combining like terms.
• Not isolating the variable $y$: Make sure to isolate the variable $y$ by adding or subtracting the same value from both sides of the equation.
• Not solving for $y$: Make sure to solve for $y$ by dividing both sides of the equation by the coefficient of $y$.

Practice Problems

To practice solving linear equations, try the following problems:

• Solve the equation $2x + 3y = 12$ when $x = 4$.
• Solve the equation $x - 2y = 5$ when $x = 3$.
• Solve the equation $3x + 2y = 10$ when $x = 2$.

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. It can be written in the form $ax + by = c$, where $a$, $b$, and $c$ are constants, and $x$ and $y$ are variables.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to follow these steps:

1. Substitute the value of $x$ into the equation.
2. Simplify the equation by evaluating any expressions and combining like terms.
3. Isolate the variable $y$ by adding or subtracting the same value from both sides of the equation.
4. Solve for $y$ by dividing both sides of the equation by the coefficient of $y$.

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(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, $x + 2y = 5$ is a linear equation, while $x^2 + 2xy + y^2 = 10$ is a quadratic equation.

Q: Can I use a calculator to solve a linear equation?

A: Yes, you can use a calculator to solve a linear equation. However, it's always a good idea to check your work by hand to make sure you understand the solution.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to follow these steps:

1. Find the $x$-intercept by setting $y = 0$ and solving for $x$.
2. Find the $y$-intercept by setting $x = 0$ and solving for $y$.
3. Plot the $x$-intercept and $y$-intercept on a coordinate plane.
4. Draw a line through the two points to represent the linear equation.

Q: Can I use a graphing calculator to graph a linear equation?

A: Yes, you can use a graphing calculator to graph a linear equation. Simply enter the equation into the calculator and press the "graph" button.

Q: What is the slope of a linear equation?

A: The slope of a linear equation is a measure of how steep the line is. It can be calculated using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

Q: How do I find the slope of a linear equation?

A: To find the slope of a linear equation, you need to follow these steps:

1. Find two points on the line.
2. Calculate the difference in $y$-values between the two points.
3. Calculate the difference in $x$-values between the two points.
4. Divide the difference in $y$-values by the difference in $x$-values to find the slope.

Q: What is the $y$-intercept of a linear equation?

A: The $y$-intercept of a linear equation is the point where the line crosses the $y$-axis. It can be calculated by setting $x = 0$ and solving for $y$.

Q: How do I find the $y$-intercept of a linear equation?

A: To find the $y$-intercept of a linear equation, you need to follow these steps:

1. Set $x = 0$ in the equation.
2. Solve for $y$ to find the $y$-intercept.

Q: What is the $x$-intercept of a linear equation?

A: The $x$-intercept of a linear equation is the point where the line crosses the $x$-axis. It can be calculated by setting $y = 0$ and solving for $x$.

Q: How do I find the $x$-intercept of a linear equation?

A: To find the $x$-intercept of a linear equation, you need to follow these steps:

1. Set $y = 0$ in the equation.
2. Solve for $x$ to find the $x$-intercept.

Conclusion

We hope this FAQ has been helpful in answering your questions about linear equations. Remember to practice solving linear equations and graphing them to become proficient in these skills. If you have any more questions, feel free to ask!