## Introduction

Welcome to the answer key for Lesson 14 Homework 5.3! In this article, we will explore and unlock the mathematical concepts and mysteries that were addressed in this particular homework assignment. By providing the answers and explanations, we hope to deepen your understanding and enhance your problem-solving skills. So let’s get started!

## Lesson 14 Homework 5.3 Answer Key: Exploring Mathematical Concepts

### Question 1:

The first question of Homework 5.3 asks you to solve a system of equations. The given equations are:

```
2x + 3y = 10
4x - 2y = 8
```

To solve this system, we can use either the substitution method or the elimination method. Let’s use the elimination method here. We can multiply the first equation by 2 and the second equation by 3 to create opposite coefficients for y. Now, we can add the two equations together:

```
4x + 6y = 20
12x - 6y = 24
```

Adding these two equations, we get:

```
16x = 44
x = 2.75
```

Substituting this value back into the first equation, we can solve for y:

```
2(2.75) + 3y = 10
5.5 + 3y = 10
3y = 4.5
y = 1.5
```

Therefore, the solution to the system of equations is x = 2.75 and y = 1.5.

By exploring the mathematical concepts in Question 1, we have successfully solved a system of equations using the elimination method. This demonstrates the importance of having multiple strategies for problem-solving and reinforces the idea that there is often more than one way to approach a mathematical problem. Remember to practice these methods to strengthen your skills and become more confident in your abilities.

## Lesson 14 Homework 5.3 Answer Key: Unlocking Mathematical Mysteries

### Question 2:

The second question in Homework 5.3 challenges you to find the slope-intercept form of a linear equation. The equation given is:

`3x - 2y = 8`

To find the slope-intercept form, we need to isolate y. We can start by subtracting 3x from both sides of the equation:

`-2y = -3x + 8`

Next, we divide both sides by -2 to solve for y:

`y = (3/2)x - 4`

So the slope-intercept form of the linear equation is y = (3/2)x – 4. This form allows us to easily identify the slope (3/2) and the y-intercept (-4), which are crucial in understanding the behavior and characteristics of the line.

### Conclusion

By unlocking the mathematical mystery in Question 2, we have successfully transformed a given equation into the slope-intercept form. This form provides valuable information about the slope and y-intercept, which can help us analyze the graph and make predictions. Remember to practice converting equations into different forms to strengthen your algebraic skills and gain a deeper understanding of linear equations. Stay curious and keep exploring the fascinating world of mathematics!