Embibe Experts Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: Nagaland Board-2018

Solve graphically the system of equations $2x-3y-17=0$, $4x-y-13=0$ and shade the region between the lines and the $x-$axis.

The present age of a woman is $3$ years more than three times the age of her daughter. Three years later, the woman’s age will be $10$ years more than twice the age of her daughter. Find their present ages. 

Solve the system of equations $2x+3y=17$ and $3x-2y=6$ using cross-multiplication method.

Solve the following pair of equation by reducing them to a pair of linear equations:

$\frac{1}{3x+y}+\frac{1}{3x-y}=\frac{3}{4}$

$\frac{1}{2\left(3x+y\right)}-\frac{1}{2\left(3x-y\right)}=\frac{-1}{8}$

A train covered a certain distance at a uniform speed. If the train had been $10 \mathrm{km}/\mathrm{hr}$ faster, it would take $2 \mathrm{hours}$ less than the scheduled time. And if the train were slower by $10 \mathrm{km}/\mathrm{hr}$, it would have taken $3 \mathrm{hours}$ more than the scheduled time. Find the distance covered by the train.

Solve the following pair of linear equations by elimination method:
$3x-5y-4=0$ and $9x=2y+7$ .

Mary travels $300 \mathrm{km}$ to her home partly by train and partly by bus. She takes $4$ hours if she travels $60 \mathrm{km}$ by train and the remaining by bus. If she travels $100 \mathrm{km}$ by train and the remaining by bus, she takes $10$ minutes longer. Find the speed of the train and the bus separately.

If $\mathrm{P}(x,y)$ is any point on the line joining the points $\mathrm{A}(a,0)$ and $\mathrm{B}(0,b),$ then show that$:\frac{x}{a}+\frac{y}{b}=1.$