A linear equation is an algebraic equation that involves a constant and a first-order term. The equation is written as y=mx+b, where m is the slope and b is the y-intercept.  Here are some examples of linear equations: y = 3 + 2x y = -0.01 + 1.2x y = 25 + 20x 2x + y - 3 = 0  The graph of a linear equation is a straight line. The slope of a line is the amount by which it rises or falls. It is calculated by the formula rise/run.  Here are some steps for solving linear equations: Expand brackets Group like terms together Simplify the equation Remove constants from the variable Check... Show more

A linear equation is an algebraic equation that involves a constant and a first-order term. The equation is written as y=mx+b, where m is the slope and b is the y-intercept. 

Here are some examples of linear equations:
y = 3 + 2x
y = -0.01 + 1.2x
y = 25 + 20x
2x + y - 3 = 0 

The graph of a linear equation is a straight line. The slope of a line is the amount by which it rises or falls. It is calculated by the formula rise/run. 

Here are some steps for solving linear equations:
Expand brackets
Group like terms together
Simplify the equation
Remove constants from the variable
Check the answer 

Linear equations can be used for many real-world applications, such as:
Calculating the outside temperature from the number of times crickets chirp in one minute
Figuring out how fast a projectile is moving
Converting one unit of measure to another
Calculating rates, such as how quickly a chemical reaction is proceeding.

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Algebra Practice Test: Linear Equations

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25 Questions

1. One added to eight times the sum of its two digits gives that number. This number is also obtained by adding 2 to 13 times the difference of its digits. Find the number.

36415738

2. The sum of two numbers is 80. If the larger number exceeds four times the smaller one by 5, then the smaller number is?

1525205

3. If the sum of two numbers is 93 and their difference is 9, find the numbers.

(42, 51)(40, 53)(43, 50)(41, 52)

4. If 1 is added to both the numerator and denominator of a fraction it becomes . If 3 is subtracted from both the numerator and the denominator it becomes . Find the fraction.

5. A boy is now ‘a’ years old, and his father is ‘5a’ years old. How old will the father be when the boy is 3a years old?

9a8a7a4a

6. Ram can row a boat 8 km downstream and return in 1 hour 40 minutes. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.

1214910

7. 4x + 3y = 8xy, 6x + 5y = 13xy

(3, 2)(2, 1)none(1, 2)

8. A number consists of two digits. When it is divided by the sum of the digits, the quotient is 7. The sum of the reciprocals of the digits is 9 times the reciprocal of the number. Find the number.

36846372

9.

(-4, -5)(3, -8)(5, 1)(8, 3)

10. In the first half of a football match, India scored ‘a’ goals and Sikkim scored ‘b’ goals. In the second half India did not score, but Sikkim scored ‘c’ goals and won the match by 2 goals. Write down an equation involving a, b, and c.

a + b = c + 2a + b + c = 2noneb + c = a

11. If 3 chairs and 2 tubes cost $1200 and 5 chairs and 3 tubes cost $1900, then the cost of 2 chairs and 2 tubes is

$700$1000$900$1100 l4.

12. The present age of a father is equal to the sum of ages of his 5 children. 12 years hence the sum of ages of his children will be twice the age of their father. Find the present age of father.

32304036

13. 2x 3y = 7,

(5, 2)(7, 5)none(3, 1)

14. Five years hence, father’s age will be three times the age of his son. Five years ago, father was seven times as old as his son. Find present age of son.

10241815

15. A purse contains only 25 paise and 50 paise coins. The total amount in the purse is $30.00. If the number of 25 paise coins is twice of the number of 10 paise coins, then the total number of coins in the purse is:

409075120

16. A number consists of two digits, whose sum is 10. If 18 is subtracted from the number, digits interchange their places. The number is

645573 l7. 46

17. In covering a distance of 30 km A takes 2 hours more than B. If A doubles his speed, he would take 1 hour less than B. A’s speed is:

7.5 km/hr5 km/hr6.25 km/hr6 km/hr

18. One third of a number of two digits is exceeds one fourth of its successor by 1. Find the number.

19242715

19. In an election, there were 3 candidates. If the successful candidate received twice as many votes as the bottom candidate and 712 votes more than the second candidate. Out of a total votes of 7968, how many votes did the successful candidate obtain?

2472347220722872

20. A battalion of soldiers, when formed into a solid square, has sixteen men fewer in the front than they do when formed in a hollow square four rows deep. Find the required number of men.

676525900576

21. The total cost of 6 books and 4 pencils is $34 and that of 5 books and 5 pencils is $30. The cost of each book and pencil (in Rs.) respectively is?

5 and 11 and 61 and 56 and 1

22. There are 10 paise and 25 paise coins in a purse. If there are total of 60 coins worth Rs.8.25, find the number of coins of each kind.

(20, 40)(50, 10)(45, 15)

23. The population of a village is 5000. If the number of males increase by 5% and females by 3%, the population would grow by 202 at the end of a year. Find the number of females in the village at present?

2400220026002000

24. If A gives B $4, B will have twice as much as A: If B gives A $15, A will have 10 times as much as B. How much B has?

18161215

25.

(2, 3)(3, 2)(4, 3)