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. A sailor goes 8 km downstream in 40 minutes and returns in 1 hour. Find the speed of the sailor in still water.

86410

2. 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?

2872207234722472

3. 2x + 3y = 5, 4x + 6y = 10

(1, 2)no solution(5, 7)(3, 4)

4. A distributes $180 in equal sums amongst a certain number of people. B distributes the same sum but gives to each person $6 more than A, and gives to 40 persons less than A does. How much does A give to each person?

$2$4$3$8

5. 5 apples and 9 oranges together cost $26 and 9 apples and 5 oranges together cost $30. Find the price of 1 apple and 1 orange.

$5$4$2$3

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

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

7. 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.

1012149

8. There are two examination halls, P and Q. If 10 students are sent from P to Q, then the number of students in each room is the same. If 20 students are sent from Q to P, then the number of students in P is double of that in Q. The number of students in P and Q respectively are:

100 , 8080, 60105 , 75 l9. 70, 50

9. Distance between two stations is 75 km apart. A train starts from a station A for station B and another train leaves B at the same time for A. If they move in the same direction they would cross each other in 5 hours and if they move towards each other they would take an hour only. The speed of the faster train is:

80 km/hr60 km/hr45 km/hr75 km/hr

10. In 10 years A will be twice as old as B was 10 years ago. Find the age of A if he is now 9 years elder than B.

not possible304845

11. 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?

1 and 65 and 11 and 56 and 1

12. The area of a rectangle remains unchanged if its length is increased by 5 m and breadth decreased by 3m. If we increase the length by 10m and decrease the breadth by 3m, the area is increased by 60m2. The length of the rectangle is:

48 m25 m28.5 m30 m

13. 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.

nonea + b = c + 2a + b + c = 2b + c = a

14. x + y = 3, x y = 1

(2, 1)(3, 1)(1 ,3)(1, 2)

15. A man wanted to exchange Rs.1000 in two types of notes of $5 and $10 denominations. If he got 180 notes in all, find the number of notes of each denomination.

(150, 30)(155, 35)(160, 20)(160, 25)

16. If 20 is reduced from twice the greater of the two numbers, the result is = to other number. If 5 is subtracted from the twice of the smaller number, 5 is subtracted the result is the first number. The larger number is:

25181215

17. If three times the larger of two numbers is divided by the smaller, the quotient and the remainder, each is equal to 6. If five times the smaller is divided by the larger, the quotient is 2 and the remainder is 3. The smaller number is:

9 l6. 786

18. 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.

576525676900

19. A man purchased 53 stamps of 20 paise and 10 paise. The total amount he spent was $8.30. The number of 20 paise and 10 paise stamps which he purchased:

18 and 3516 and 37cannot be determined from the given data30 and 23

20. 3x 4y = 10, 5x + 2y = 8

(1, 2)(3, 4)(2, 1)

21. A, B, C travel from the same place in the same direction at the rates of 20, 25, and 40 miles per hour respectively. If B starts half an hour after A, how long after A must C start in order that B and C may overtake A at the same moment.

22. 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

23. Divide 20 into four parts such that if the first increased by 1, the second diminished by 2, the third multiplied by 3 and the fourth divided by 4, the result in each case is the same. Find the greatest part.

1014512

24. If you add 1 to each of two given numbers then their ratio is 1:2. If I subtract 5 from each, the ratio is 5:11, find the numbers.

(60, 119)(35, 69)(31, 61)(33, 67)

25. 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:

6.25 km/hr5 km/hr7.5 km/hr6 km/hr