Embibe Experts Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: CBSE-2019

In Fig. 1, $ABCD$ is a rectangle. Find the values of $x$ and $y$.

Find $c$ if the system of equations $cx+3y+\left(3-c\right)=0$; $12x+cy-c=0$ has infinitely many solutions.

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.

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.

A boat goes $30 \mathrm{km}$ upstream and $44 \mathrm{km}$ downstream in $10$ hours. In $13$ hours, it can go $40 \mathrm{km}$ upstream and $55 \mathrm{km}$ downstream. Determine the speed of the stream and that of the boat in still water.

Determine graphically the coordinates of the vertices of a triangle, the equations of whose sides are given by $2y-x=8$,$5y-x=14$ and $y-2x=1$.

The value of $k$ for which the system of equations $x+y-4=0$ and $2x+ky=3$, has no solution is 

The sum of two numbers is $34$. If $3$ is subtracted from one number and $2$ is added to another, the product of these two numbers becomes $260$. Find the numbers.