Practice the problems of Math in Focus Grade 8 Workbook Answer Key Chapter 5 Lesson 5.1 Introduction to Systems of Linear Equations to score better marks in the exam.

## Math in Focus Grade 7 Course 3 A Chapter 5 Lesson 5.1 Answer Key Introduction to Systems of Linear Equations

### Math in Focus Grade 8 Chapter 5 Lesson 5.1 Guided Practice Answer Key

**Solve the system of linear equations by copying and completing the tables of values.
The values x and y are positive integers.**

Question 1.

A bottle of water and a taco cost $3. The cost of 3 bottles of water is $1 more than the cost of a taco.

Let x be the price of a bottle of water and y be the price of a taco in dollars.

The related system of equations and tables of values are:

3x – y = 1

x + y = 3

Answer:

The cost of a bottle of water is $2 and the cost of a taco is $1,

Explanation:

**Solve each system of equations by making tables of values, x and y are positive integers.**

Question 2.

x + y = 6

x + 2y = 8

Answer:

Explanation:

Solved each system of equations by making tables of values, x and y are positive integers.

For equation x+y = 6, when x =1 then y =5 and when x =2 then y=4,

For equation x +2y =8, when x =1 then y =7/2 and when x = 2 then x =3.

Question 3.

x + y = 8

x – 3y = -8

Answer:

Explanation:

Solved each system of equations by making tables of values, x and y are positive integers.

For equation x+y = 6, when x =1 then y =5 and when x =2 then y=4,

For equation x +2y =8, when x =1 then y =7/2 and when x = 2 then x =3.

**For each linear equation, list in a table enough values for x and y to obtain a solution.
Remember that they must be positive integers.**

**Technology Activity**

**Materials:**

- graphing calculator

Use Tables On A Graphing Calculator To Solve A System Of Equations

Work in pairs.

You can use a graphing calculator to create tables of values and solve systems of equations.

Use the steps below to solve this system:

8x + y = 38

x – 4y = 13

Step 1.

Solve each equation for y in terms of x. Input the two resulting expressions for y into the equation screen.

Caution

Use parentheses around fractional coefficients and the key for negative coefficients

Step 2.

Set the table function to use values of x starting at 0, with increments of 1.

Step 3.

Display the table. It will be in three columns as shown.

Step 4.

Find the row where the two y-values are the same. This y-value and the corresponding x-value will be the solutión to the equations.

The solution to the system of equations is given by x = and y = .

Math Journal How can you tell from the two columns of y-values that there is only one row where the y-values are the same?

### Math in Focus Course 3A Practice 5.1 Answer Key

**Solve each system of linear equations by making tables of values.
Each variable x is a positive integer less than 6.**

Question 1.

2x + y = 5

x – y = -2

Answer:

Explanation:

Solved each system of linear equations by making tables of values.

Each variable x is a positive integer less than 6.

Question 2.

x + 2y = 4

x = 2y

Answer:

Explanation:

Solved each system of linear equations by making tables of values.

Each variable x is a positive integer less than 6.

Question 3.

3x + 2y = 10

5x – 2y = 6

Answer:

Explanation:

Solved each system of linear equations by making tables of values.

Each variable x is a positive integer less than 6.

Question 4.

x – 2y = -5

x = y

Answer:

Explanation:

Solved each system of linear equations by making tables of values.

Each variable x is a positive integer less than 6.

Question 5.

2y – x = -2

x + y = 2

Answer:

Explanation:

Solved each system of linear equations by making tables of values.

Each variable x is a positive integer less than 6.

Question 6.

2x + y = 3

x + y = 1

Answer:

Explanation:

Solved each system of linear equations by making tables of values.

Each variable x is a positive integer less than 6.

Question 7.

x + 2y = 1

x – 2y = 5

Answer:

Explanation:

Solved each system of linear equations by making tables of values.

Each variable x is a positive integer less than 6.

Question 8.

2x – y = 5

2y + x = -1

Answer:

Explanation:

Solved each system of linear equations by making tables of values.

Each variable x is a positive integer less than 6.

Question 9.

2x + y = -1

x + y = 1

Answer:

Explanation:

Solved each system of linear equations by making tables of values.

Each variable x is a positive integer less than 6.

**Solve by making a table of values. The values x and y are integers.**

Question 10.

A shop sells a party hat at x dollars and a mask at y dollars.

On a particular morning, 10 hats and 20 masks were sold for $30.

In the afternoon, 8 hats and 10 masks were sold for $18. The related system of linear equations is:

10x + 20y =30

8x + 10y = 18

Solve the system of linear equations. Then find the cost of each hat and each mask.

Answer:

The cost of each hat is $1 and each mask is$1,

Explanation:

Given A shop sells a party hat at x dollars and a mask at y dollars.

On a particular morning, 10 hats and 20 masks were sold for $30.

In the afternoon, 8 hats and 10 masks were sold for $18.

The related system of linear equations is:

10x + 20y =30—(1)

8x + 10y = 18—-(2) dividing equation 1 by 10 we get

x +2y = 3,

x = 3-2y substituting in equation 2 we get

8(3-2y) +10y =18,

24 – 16y+10y =18,

24 -6y =18,

6y = 24 -18,

6y =6, y =1 we have x = 3-2X 1 = 3-2 = 1.

Question 11.

Alicia is x years old and her cousin is y years old.

Alicia is 2 times as old as her cousin.

Three years later, their combined age will be 27 years.

The related system of linear equations is:

x = 2y

x + y = 27

Solve the system of linear equations. Then find Alicia’s age and her cousin’s age.

Answer:

Alicia’s age is 18 and her cousin’s age is 9 years old,

Explanation:

GivenAlicia is x years old and her cousin is y years old.

Alicia is 2 times as old as her cousin.

Three years later, their combined age will be 27 years.

The related system of linear equations is: x = 2y,

x + y = 27 solving the equations 2y + y = 27,

3y = 27, y = 27/3 =9, so x = 2X 9 = 18, Alicia’s age is 18 and her

cousin’s age is 9 years old.

Question 12.

Steve and Alex start driving at the same time from Boston to Paterson.

The journey is d kilometers. Steve drives at 100 kilometers per hour and

takes t hours to complete the journey. Alex, who drives at 80 kilometers per hour is

60 kilometers away from Paterson when Steve reaches Paterson.

The related system of linear equations is:

100t = d

80t = d – 60

Solve the system of linear equations by making tables of values.

Then find the distance between Boston and Paterson.

Answer:

300 kilometers is the distance between Boston and paterson,

Explanation:

Given Steve and Alex start driving at the same time from Boston to Paterson.

The journey is d kilometers. Steve drives at 100 kilometers per hour and

takes t hours to complete the journey. Alex, who drives at 80 kilometers per hour is

60 kilometers away from Paterson when Steve reaches Paterson.

The related system of linear equations is:

100t = d

80t = d – 60 substituting 80t = 100t -60,

100t-80t = 60,

20t = 60, t = 60/20, t =3 so distance is 100 X 3= 300 kilometers.