Pair of Linear Equations in Two Variables - Class 10 CBSE

Pair of Linear Equations in Two Variables - Class 10 CBSE

by

Salman Nizarudin

Multiple Choice

How many solutions does the pair of equations y = 0 and y = -5 have, and what is the shape of lines represented? (2013)

• One single line, infinite solutions

• Intersecting lines, one solution

• Parallel lines, no solution

• Perpendicular lines, one solution

Multiple Choice

If  $ax+by=a^2-b^2$ and  $bx+ay=0$ , find the value of  $\left(x+y\right)$ . (2013)

•  $a-b$  

•  $a+b$  

•  $a^2-b^2$  

•  $a^2+b^2$  

Multiple Choice

For what value of k, the pair of equations 4x – 3y = 9, 2x + ky = 11 has no solution? (2017D)

• $\frac{3}{2}$

• $\frac{-2}{3}$

• $\frac{2}{3}$

• 
  

  $\frac{-3}{2}$
  

Multiple Choice

Calculate the area bounded by the line x + y = 10 and both the co-ordinate axes. (2012)

• 
  

  $100\ cm^2$
  

• $75\ cm^2$

• $50\ cm^2$

• $25\ cm^2$

Multiple Choice

Solve for x and y:  $\frac{10}{x+y}+\frac{2}{x-y}=4$    and 
 $\frac{15}{x+y}-\frac{5}{x-y}=-2$  ;       x + y ≠ 0  ,   x – y ≠ 0 (2012, 2017D)

•  $x=4\ ,\ y\ =\ 1$  

•  $x=3\ ,\ y=2$  

•  $x\ =\ 6\ ,\ y\ =\ -1$  

•  $x\ =\ 5\ ,\ y\ =\ 0$  

Multiple Choice

Solve the following pair of linear equations for x and y:

141x + 93y = 189 ;

93x + 141y = 45 (2013)

• 
  

  $x\ =2\ ,\ y\ =\ -1$
  

• $x\ =\ 2\ ,\ y\ =\ 2$

• $x\ =\ -1\ ,\ \ y=\ -1$

• $x=-1\ ,\ y=2$

Fill in the Blank

Find the two numbers whose sum is 75 and difference is 15. (2014)

[ENTER ANSWER WITH COMMA SEPERATION, DO NOT ENTER SPACE]

Multiple Choice

Find the value of  $\alpha$  and  $\beta$  for which the following pair of linear equations has infinite number of solutions:
 $2x+3y=7$  ;
 $\alpha x+\left(\alpha+\beta\right)y=28$   (2013)

•  $\alpha=-8\ ,\ \beta=20$  

•  $\alpha=8\ ,\ \beta=4$  

•  $\alpha=18\ ,\ \beta=6$  

•  $\alpha=-8\ ,\ \beta=-4$  

Multiple Choice

A man earns ₹ 600 per month more than his wife. One-tenth of the man’s salary and  $\frac{1}{6}$ th of the wife’s salary amount to ₹ 1,500, which is saved every month. Find their incomes. (2014)

• Man = ₹ 3000
  Wife = ₹ 2400

• Man = ₹ 6500
  Wife = ₹ 5900

• Man = ₹ 3500
  Wife = ₹ 2900

• Man = ₹ 6000

  Wife = ₹ 5400

Fill in the Blank

The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number. (2015)

Fill in the Blank

The age of the father is twice the sum of the ages of his 2 children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father. (2012)

Multiple Choice

Sita Devi wants to make a rectangular pond on the road side for the purpose of providing drinking water for street animals. The area of the pond will be decreased by 3 square feet if its length is decreased by 2 ft. and breadth is increased by 1 ft. Its area will be increased by 4 square feet if the length is increased by 1 ft. and breadth remains same. Find the dimensions of the pond. (2014)

• Length of pond = 17 ft

  Breadth of pond = 11 ft

• Length of pond = 7 ft

  Breadth of pond = 4 ft

• Length of pond = 3 ft

  Breadth of pond = 1 ft

• Length of pond = 7 ft

  Breadth of pond = 3 ft

Multiple Choice

Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream. (2017D)

• Speed of stream = 5 km/hr

• Speed of stream = -5 km/hr

• Speed of stream = 10 km/hr

• Speed of stream = 15 km/hr

Fill in the Blank

The owner of a taxi company decides to run all the taxis on CNG fuel instead of petrol/diesel. The taxi charges in city comprises of fixed charges together with the charge for the distance covered. For a journey of 13 km, the charge paid is ₹ 129 and for a journey of 22 km, the charge paid is ₹ 210.

What will a person have to pay for travelling a distance of 32 km? (2014 )

Multiple Choice

A man travels 300 km partly by train and partly by car. He takes 4 hours if the travels 60 km by train and the rest by car. If he travels 100 km by train and the remaining by car, he takes 10 minutes longer. Find the speeds of the train and the car separately. (2017D)

• Speed of the train = 40 km/hr

  Speed of the car = 60 km/hr

• Speed of the train = 160 km/hr

  Speed of the car = 80 km/hr

• Speed of the train = 30 km/hr

  Speed of the car = 100 km/hr

• Speed of the train = 60 km/hr

  Speed of the car = 80 km/hr