# Linear Equation in One Variable

## Trending Questions

**Q.**Question 2

The pair of equation x + 2y + 5 = 0 and -3x – 6y + 1 = 0 has

(A) a unique solution

(B) exactly two solutions

(C) infinitely many solutions

(D) no solution

**Q.**

Question 78

Solve the following:

0.16(5x-2)=0.4x+7

**Q.**On her birthday, Sonia distributed chocolates in an orphanage. She gave 5 chocolates to each child and 20 chocolates to adults. Take the number of children as x and total number of chocolates distributed as y:

1) Form a linear equation.

2)If she distributed 145 chocolates in total, how many children are there in the orphanage?

3) What values are reflected in the situation?

**Q.**

**Solve the equation: **$7x-9=16$

**Q.**

Ram is five years elder to his youngest sibling Shreya. Shreya is two years younger than her brother Ritesh. Ritesh is 13 years old and is Rams brother. How old will ram be in two years from now?

**Q.**

Pat made a total of $48$ pottery plates and cups. If she made twice as many plates as cups. How many plates did she make?

**Q.**

Factorise:

x2−(a+b)x+ab

**Q.**

Question 50

Reshma prepared 18 kg of Burfi by mixing Khoya with sugar in the ratio 7 : 2. How much Khoya did she use?

**Q.**

The general form of equation in one variable is:

ax + b = 0 where a ≠ 0 and a, b are real numbers

None of these

ax + b = 0

ax + b = 0 where, a≠0

**Q.**

Which of the following represents a linear equation in two variables?

where, x is a variable and a, b are real numbers

where, a, b, c are real numbers and xy ≠ 0, and x, y are variables=

where, a, b, c are real numbers and + ≠ 0

where, a, b, c are the variables and x, y are real numbers

**Q.**

What is the standard equation of a linear equation?

**Q.**

The equation x - 2 = 0 on number line is represented by

a line

a point

infinitely many lines

two lines

**Q.**Fill in the blank with the correct option.

A linear equation in one variable is _________. Fill in the blank with the correct option.

- An equation with one term
- An equation in which the highest power of the variable is one
- An equation with two terms
- An equation with only one variable

**Q.**

If $(6,k)$ is a solution of the equation $3x+y-22=0$, then the value of $k$ is?

**Q.**

The distance between the graph of the equations x = - 3 and x = 2 is

5

1

3

2

**Q.**

The number of girls in a class is 4 more than the number of boys. On a day when only 8 boys were absent, the numbers of girls were double the number of boys. How many girls and boys are there in that class?

**Q.**How many solutions does the linear equation 3x - 5y = 15 have?

- Unique
- Two
- Infinite
- No solution

**Q.**

Kamal has $x$ children by his first wife. Ritu has $\left(\mathrm{x}+1\right)$ children by her first husband. They marry and have children of their own. The whole family has $24$ children. Assuming the two children of the same parents do not fight, then the maximum possible number of fights that can take place is :

$190$

$191$

$200$

$52$

**Q.**Find the values of n and X in each of the following cases:

(i) $\sum _{t=1}^{n}({x}_{i}-12)=-10$ and $\sum _{t=1}^{n}({x}_{i}-3)=62$

(ii) $\sum _{t=1}^{n}({x}_{i}-10)=30$ and $\sum _{t=1}^{n}({x}_{i}-6)=150$

**Q.**Form the pair of linear equations for the following problems and find their solution by substitution method:

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

**Q.**

The sum of four consecutive odd integers is $216$. What are the four integers?

**Q.**

Question 6

The product of 1113 and 4 is

(a) 3513

(b) 5313

(c) 1335

(d) 1353

**Q.**

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

2x + 3y = 10

4a + 5b = 3b + 6

2x = 3x + 4

2x + 4z = 5

**Q.**

after 5 years the age of father will be two times the age of Son.write equation in two variables to represent this statement

**Q.**Only 60% and 50% of eligible voters of town A and B respectively, cast their vote in the election. The total number of votes cast were 1200.

Which of the following linear equations represents this scenario accurately?

(Assume number of eligible voters in town A to be x and in town B to be y)

- 5x+6y=12000
- 6x+5y=12000
- 5x+6y=1200
- 6x+5y=1200

**Q.**

Question 3(e)

Fill in the blanks:

___ ÷ 1 = - 87

**Q.**

If the point P(a, 1) lies on the line 2x-3y-5=0, then find the value of a.

-4

0

2

4

**Q.**

Find the value of 'x' in the equation 3x+8=0.

x=−83

x=83

x=−8

x=8

**Q.**

A boat takes $7$ hours to travel $30$ km upstream and $28$ km downstream. It takes $5$ hours to travel $21$ km upstream and to return back. Find the speed of the boat in still water.

$10\mathrm{km}/\mathrm{hr}$

$20\mathrm{km}/\mathrm{hr}$

$14\mathrm{km}/\mathrm{hr}$

$6\mathrm{km}/\mathrm{hr}$

**Q.**

A father is three times as old as his son. In $12$ years time, he will be twice as old as his son. Find the present ages of father and the son.