In Fig. 1, A B C D is a rectangle. Find the values of x and y .

Given figure is, We know that, opposite sides of a rectangle are equal. ⇒ x + y = 30 ...(i) and x - y = 14 ....(ii) On adding Eqs. ( i ) and ( i i ) we get 2 x = 30 + 14 ⇒ 2 x = 44 ⇒ x = 44 2 = 22 cm On putting x = 22 in Eq. ( i ) , we get 22 + y = 30 ⇒ y = 30 - 22 = 8 cm Hence, values of x and y are 22 cm and 8 cm respectively.

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Pair of Linear Equations in Two Variables>CBSE-2019>Q 3

MEDIUM

10th CBSE

IMPORTANT

Earn 100

A father's age is three times the sum of the ages of his two children. After $5$ years, his age will be two times the sum of their ages. Find the present age of the father.

Important Questions on Pair of Linear Equations in Two Variables

EASY

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Pair of Linear Equations in Two Variables>CBSE-2019>Q 4

A fraction becomes

\frac{1}{3}

when

2

is subtracted from the numerator and it becomes

\frac{1}{2}

when

1

is subtracted from the denominator. Find the fraction.

HARD

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Pair of Linear Equations in Two Variables>CBSE-2019>Q 5

A boat goes

30 km

upstream and

44 km

downstream in

10

hours. In

13

hours, it can go

40 km

upstream and

55 km

downstream. Determine the speed of the stream and that of the boat in still water.

MEDIUM

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Pair of Linear Equations in Two Variables>CBSE-2020>Q 6

Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are given by

2 y - x = 8

,

5 y - x = 14

and

y - 2 x = 1

.

EASY

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Pair of Linear Equations in Two Variables>CBSE-2020>Q 7

The value of

k

for which the system of equations

x + y - 4 = 0

and

2 x + k y = 3

, has no solution is

MEDIUM

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Pair of Linear Equations in Two Variables>CBSE-2021 (Delhi - I)>Q 8

The values of

x

and

y

satisfying the two equations

32 x + 33 y = 34, 33 x + 32 y = 31

, respectively are:

MEDIUM

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Pair of Linear Equations in Two Variables>CBSE-2021 (Delhi - I)>Q 9

Two lines are given to be parallel. The equation of one of the lines is

3 x - 2 y = 5

. The equation of the second line can be:

HARD

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Pair of Linear Equations in Two Variables>CBSE-2021 (Delhi - I)>Q 10

In a

∆ ABC, ∠ A = x °, ∠ B = (3 x - 2) °, ∠ C = y °

. Also,

∠ C - ∠ B = 9 °

. The sum of the greatest and the smallest angles of this triangle is:

EASY

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 3 - Pair of Linear Equations in Two Variables>CBSE-2022 (Delhi - II)>Q 12

A $2 -$ digit number is such that the product of its digits is $24$ . If $18$ is subtracted from the number, the digits interchange their places. Find the number.