Linear Equation

Q. Suraj and Aditya bought a certain number of pencils that cost Rs 3 each. The number of pencils that Suraj bought is 10 greater than 4 times the number of pencils that Aditya bought. The total cost of pencils that Suraj bought is Rs 162. Find the number of pencils that Aditya bought.

1. 38
2. 16
3. 11
4. 54

Q.

At a certain time in a deer park, the number of heads and number of legs of deer and human visitors was counted and it was found that there were $39$ heads and $132$ legs. Find the number of deers and human visitors in the park.

Q.

What do you mean by linear equation?

Q. Which of the following equation is a linear equation in one variable?

1. 2x + 3y = 10
2. 2x = 3x + 4
3. 2x + 4z = 5
4. 2x = 3y + 4

Q.

ax+b=0, a≠0

Q.

x = −5 can be expressed as a linear equation in 2 variables.

1. True

2. False

Q.

Which of the following equation(s) is\are linear equation(s) in one variable?

1. 2x + 3y = 10

2. 4a + 3b = 6

3. 2x = 3x + 4

4. 2x + 4z = 5

Q. Three times the age of Rama is 15.

Which of the following equations represents the given statement mathematically?
(Assuming the age of Rama to be '$x$')

1. $\frac{x}{15}=3$
   
2. $3x=15$
3. $15x=3$
4. $\frac{1}{15}+\frac{1}{x}=\frac{1}{3}$
   

Q. The present age of Vinay’s mother is three times the present age of Vinay. After 5 years, sum of their ages will be 70 years. Find their present ages.
[3 marks]

Q. Amit is three years elder to his sister five years ago, three fifths of his age was equal to three fourths of her age. How old are Amit and his sister how?

Q. Which of the following is a linear equation in one variable?

1. $xy+5$
2. $x+4=0$
3. $x^3+3=0$
4. $x+2$

Q. Solve for $x$:
$\frac{3}{x+1}-\frac{2}{x-1}=\frac{5}{x^2-1}$

1. 9
2. 10
3. 12
4. 8

Q.

All algebraic equations that have its degree greater than one are linear equations.

1. True

2. False

Q. Give the geometric representation of 2x + 9 = 0 as an equation:
(i) in one variable
(ii) in two variables

Q. Which of the following pair is a solution of the equation $2x-y=7$?

1. $(5,1)$
2. $(1,5)$
3. $(0,2)$
4. $(2,-3)$

Q.

What is the value of $8-4x$ when $x=-3$?

Q. A number is $6$ more than another number. The sum of the two numbers is $24$. Find the numbers.

Q.

The average of three numbers is their sum multiplied by 3.

1. True

2. False

Q. Solve: $\frac{t+2}{3}+\frac{1}{t+1}=\frac{t+3}{2}-\frac{t-1}{6}$.

1. $t=\frac{1}{2}$
2. $t=-2$
3. $t=2$
4. $t=0$

Q.

A motorboat covers a certain distance downstream in a river in 4 hours. It covers the same distance upstream in 5 hours. The speed of the motorboat in still water is 27 km/h.

What is the speed of the stream?

Q. The total number of variables in the equation 3a + b + 6ab = 0 is 2.

1. False
2. True

Q. The value of x in the equation 5x = 5 is 5.

1. True
2. False

Q. The sum of two numbers exceeds thrice the smaller by $2$. If the difference between them is $19$, find the numbers

Q. Which of the following equation is a linear equation in one variable?

1. 2x + 3y = 10
2. 2x = 3x + 4
3. 2x = 3y + 4
4. 2x + 4z = 5

Q. The sum of the digits of a two-digit number is 7. If the number formed by interchanging the digits is less than the original number by 27, then find the original number. (3 marks)

Q. Which of the following is a linear equation in one variable?

1. $xy+5$
2. $x+2$
3. $x+4=0$
4. $x^3+3=0$

Q. Which of the following is a linear equation in one variable?

1. $x+4=0$
2. $x^3+3=0$
3. $x+2$
4. $xy+5$

Q. If the tens digit is twice the units digit in the number 'ab'. Choose the correct option.

1. a = 2b
2. b = 2a
3. a = b
4. a = 0.2 b

Q. Which of the following equation is a linear equation in one variable?

1. 2x + 3y = 10
2. 2x = 3x + 4
3. 2x = 3y + 4
4. 2x + 4z = 5

Q.

Which of the following equation(s) is/are linear equation(s) in one variable?

1. 2x + 3y = 10

2. 4a + 3b = 3b + 6

3. 2x = 3x + 4

4. 2x + 4z = 5