Linear Equations in One Variable

Q. Question 17
How many linear equations in x and y can be satisfied by x = 1 and y = 2?

A) Only one
B) Two
C) Infinitely many
D) Three​​​​​​​

Q.

Mr. Mukharjee gave 5/14 of his money to his son, 2/3 of the remainder to his daughter and rest to his wife. If his wife got Rs. 36000/-, what was the total amount?

Q.

Find the value of x which satisfies the given equation.
$3x+5=17$

1. $x=44$

2. $x=12$

3. $x=\frac{4}{3}$

4. $x=4$

Q.

Assertion: The degree one polynomial equation $ax+by+c=0$ is called a linear equation.

Reason : The geometrical representation of a degree one polynomial, equation is straight line.

Which of the following is correct?

1. Both A and R are true and R is not the correct explanation of A.

2. Both A and R are true and R is the correct explanation of A.

3. A is true and R is false.

4. A is false and R is true.

Q.

Elizabeth has $\$10,\$5,\text{and}\$1$ bills worth $\$101$.

She has five more five dollar bills than ten dollar bills and $4$ times more $1$ dollar bills than $10$ dollar bills.

How many of each kind of bills does Elizabeth have?

Q.

Ramesh and Suresh are $20$ years old and $12$ years old respectively. Find how many years ago, the age of Ramesh was twice that of Suresh.

Q.

If $\frac{2x}{9}=8$, what is the value of $x$ which balances the equation?

1. $x=3$

2. $x=72$

3. $x=36$

4. $x=9$

Q. I have x apples. My friend has six more than 3 times the number of apples I have. The number of apples my friend has is

1. $x+6$
2. $3x$
3. $3x+6$
4. $6x+3$

Q.

In the equation $\frac{2x}{9}=8$, what is the value of $x$ which balances the equation?

1. $x=72$

2. $x=3$

3. $x=9$

4. $x=36$

Q. In a linear equation, the highest power of variable is ___.

1. 3
2. 0
3. 1
4. 2

Q. Which of the following is/are linear equations?

1. $2x+3$
2. $2x^2+3$
3. $2x+3=0$
4. Both B and C

Q. Solve: $\frac{y+2}{3}+\frac{y+5}{4}=6$

Q.

The present age of Pratik and Arjun are in the ratio 2 : 3. After 4 years, the ratio of their age will be 4 : 5. The present age of Arjun is

1. 5

2. 10

3. 15

4. 20

Q. Convert the following equations in statement form:
a)$\frac{m}{5}-2=6$ b) 5p = 20 c) 3n + 7 = 1

Q. The graph of the following linear equations in two variables :
$x+y=4$

Q.

abhi gave his cousin one third of his sticker collection he gave his sister 56 of the remainder and was left with 80 stickers how many stickers did he have at first?

Q.

Explain the process to solve the equation. Use proper vocabulary in your explanation. $\frac{1}{4}x=\frac{5}{8}$

Q. A number (n) when added to 14 gives 72.
Which of the following represents the above statement mathematically?

1. 14n = 72
2. 14 - n = 72
3. n + 14 = 72
4. 72n = 14

Q.

One day Krishnayya and his 10-year-old granddaughter Subbu are having the following conversation:

Subbu: Grandpa, When were you born?
Krishnayya then gave a Mathematical puzzle to his granddaughter to solve.

Grandfather: Kid, I am 8 more than 6 times your age by now (2015).
Subbu started thinking. Being good at Mathematics, Subbu screamed her grandpa's year of birth in less than a minute.
Which year do you think he was born?

___

Q.

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

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

Q. Find the value of $x$ which balances the equation $\frac{2x}{9}=8$.

1. 36
2. 72
3. 3
4. 9

Q.

$x+2x^2=3$ is a linear equation because the power of 'x' is 1.

1. True

2. False

Q. Indian cricket team won 4 more matches than it lost to New Zealand. If it won ${\frac{3}{5}}^{\text{th}}$ of its matches, how many matches did India play ?

1. 20
2. 8
3. 40
4. 30

Q. Find the value of $x$ which balances the equation $\frac{2x}{9}=8$.

1. 9
2. 72
3. 36
4. 3

Q. In a linear equation, the highest power of variable is ___.

1. 0
2. 3
3. 1
4. 2

Q. The ratio of the present ages of Rahim and his wife is 4:3. After 4 years the ratio of their ages will be 9:7. Then find the present age of Rahim.

1. 36
2. 34
3. 30
4. 32

Q. Find the value of a and b if b is four more than the half of a and a = b.
The answer is given that the value of both a and b is 8 but I didn't understand the method.

Q.

The ratio $\frac{\text{number of oranges I have}}{\text{number of oranges my friend has}}$ is equal to $\frac{2}{3}$ We know that I have $x$ oranges and my friend has $2x-3$ oranges. How do we represent this as an equation?

1. $x(2x-3)=\frac{2}{3}$

2. $\frac{2x}{x-3}=\frac{2}{3}$

3. $\frac{x}{2x-3}=\frac{2}{3}$

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

Q. Find the value of $x$ which balances the equation $\frac{2x}{9}=8$.

1. 3
2. 72
3. 9
4. 36

Q.

State which of the following are equation. Give reason for your answer. Answer which variable is used in the equation with a variable.
$9y+6=12$