# Hotmath Practice Problems

Title:
Hotmath Pre-Algebra
Author:
Hotmath Team
Chapter:Linear Equations and InequalitiesSection:Systems of Linear Equations and Inequalities

Problem: 1

Write a system of linear equations that represents the following:

The difference of two numbers x and y is 6, and the product of 3 and x is y.

Problem: 3

Write a system of linear equations that represents the conditions.

The sum of two numbers x and y is 2, and y is equal to 5 times x.

Problem: 5

Determine the solution of the system of equations from the given sketches.

b and c

Problem: 7

Determine the solution of the system of equations from the given sketches.

c and the x–axis

Problem: 9

Determine the solution of the system of equations from the given sketches.

c,b, and d

Problem: 11

Check whether (–2, 8) is a solution of the system of equations? Explain your work.

y = –3x + 2

y = x – 6

Problem: 13

Graph the system of linear equations. Then find the solution.

y = 5 – x

x = y + 1

Problem: 15

Graph the system of equations. Then find the solution.

x = 4

y = x + 2

Problem: 17

Find the solution of the given system of equations using the graph.

y = x + 4

y = 2x

Problem: 19

y = x

y = 5x – 8

Problem: 21

Solve the system of equations by graphing.

y = x + 2

y = –x – 4

Problem: 23

3x – 6y = 61

y = 0.5x – 1

Problem: 25

Find the solution of the given system of equations using the graph.

3/8x + 1/6y = 6

x = –4/9y + 16

Problem: 27

Solve the system using a graph. Check whether the lines intersect or coincide, or are parallel.

xy = –4

xy = 3

Problem: 29

Solve the system using a graph. Check whether the lines intersect or coincide, or are parallel.

–3y – 3x = –12

x + y = 4

Problem: 31

Solve the given system of equations.

y = x + 3, y = 5x + 23, and y = –3x – 17

Problem: 33

Write a system of linear equations. Then graph the system and find the solution.

The sum of two numbers x and y is 30, and y is 5 more than four times x.

Problem: 35

Write a system of linear inequalities that represents the conditions.

The sum of twice a number x and three times another number y is greater than 6, and y is less than three times x.

Problem: 37

Graph the system of linear inequalities.

y x

y 3x + 4

Problem: 39

Graph the system of linear inequalities.

y x – 3

y x + 1

Problem: 41

Graph the system of linear inequalities. Then identify three solutions.

x – (7/2) y

y x + 4

Problem: 43

Graph the system of inequalities. Then identify three solutions.

y x + 2

y x – 5

Problem: 45

Graph the system of inequalities. Then identify three solutions.

x 5 – y

y x + 4

Problem: 47

Write a system of linear inequalities. Then graph the system and identify three solutions.

The difference of two numbers x and y is less than 12, and the sum of y and three times x is greater than 4.

Problem: 49

Obtain a system of linear inequalities to describe the graph.

Problem: 51

Graph each system of equations. What can you determine about the solution of each system?

y = x + 4

y = x – 4

Problem: 53

Find the values of A and B for the system of equations Ax + y = 5 and Bx + y = 9

if the solution is (1, 1)?

Problem: 55

Is (0, 2) a solution of the system of linear equations y = 3x + 2and 4y – 8 = x?

Problem: 57

The total points for a test is 156 and there are 15 questions. Each question is worth 6 points or 12 points.

a) Let x be the number of 6–point questions and

Let y be the number of 12–point questions.

Write a system of equations to find the number of each type of question.

b) Solve the system by graphing.

c) How many questions of each type are on the test?

Problem: 59

Find two numbers whose sum is –5 and difference is 3. Let the greater number be x and the lesser number be y.

Problem: 61

The length of a rectangle is four times its width. Find the area of the rectangle if its perimeter is 30 ft.