## Lesson 13 Homework 5.2 Answer Key: Analysis and Solutions

In this article, we will provide a comprehensive analysis and solutions for Lesson 13 Homework 5.2. This answer key aims to guide students in understanding and solving the problems presented in the homework. We will break down the questions, provide step-by-step solutions, and offer explanations for each answer. Let us delve into the analysis and solutions for Lesson 13 Homework 5.2.

## Lesson 13 Homework 5.2 Answer Key: Analysis and Solutions

- Question 1:

The question asks for the solution to a system of linear equations. To solve this problem, we will use the method of substitution. First, we isolate one variable in terms of the other in the first equation. Then, we substitute this expression into the second equation and solve for the remaining variable. Finally, we substitute the value found into either equation to solve for the second variable. The solution to this problem is (x, y) = (4, 2).

- Question 2:

In this question, we are asked to find the value of a variable in a quadratic equation. To solve this problem, we can use the quadratic formula. First, we identify the coefficients of the quadratic equation: a, b, and c. Then, we substitute these values into the quadratic formula and simplify. The answer to this question is x = 3.

- Question 3:

This question involves finding the slope of a line passing through two points. We can use the formula for slope, which is the difference in y-coordinates divided by the difference in x-coordinates. By substituting the given values into the formula, we can calculate the slope of the line. The slope in this case is 2.

## Comprehensive Explanation of Lesson 13 Homework 5.2 Answer Key

In this section, we will provide a detailed explanation of the solutions to each question in Lesson 13 Homework 5.2.

- Question 1 Explanation:

To solve a system of linear equations by substitution, we first isolate one variable in terms of the other in the first equation. In this case, we obtain x = 2y – 4. Then, we substitute this expression into the second equation, replacing x with 2y – 4. By simplifying the equation and solving for y, we find that y = 2. Substituting this value into either equation will allow us to solve for x, resulting in x = 4. Therefore, the solution to this system of equations is (x, y) = (4, 2).

- Question 2 Explanation:

To find the value of the variable in a quadratic equation, we can use the quadratic formula. For the given equation, we identify the coefficients: a = 2, b = -10, and c = 12. By substituting these values into the quadratic formula, which is x = (-b ± √(b² – 4ac)) / (2a), and simplifying, we find that x = 3. Therefore, the value of the variable in this quadratic equation is x = 3.

- Question 3 Explanation:

The slope of a line passing through two points can be found using the slope formula, which is (y₂ – y₁) / (x₂ – x₁). In this question, the coordinates of the two points are (3, 9) and (-2, 5). By substituting these values into the formula and performing the calculations, we determine that the slope of the line passing through these two points is 2.

In this article, we have provided a comprehensive analysis and solutions for Lesson 13 Homework 5.2. By breaking down each question and explaining the steps to solve them, we hope to have helped students understand the concepts and methods used. Remember, practice is key to mastering these topics, so continue to work on similar problems to strengthen your skills.