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

We have a linear equation $2x+3y-8=0$. Write another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines.

Now, write two more linear equations, so that one forms a pair of parallel lines and the second forms a coincident line with the given equation.

Solve the following pairs of equations by reducing them to a pair of linear equations.

$\begin{array}{l}\frac{5}{x-1}+\frac{1}{y-2}=2\\ \frac{6}{x-1}-\frac{3}{y-2}=1\end{array}$

An algebra textbook has a total of $1382$ pages. It is broken up into two parts. The second part of the book has $64$ pages more than the first part. How many pages are in each part of the book?

The taxi charges in Hyderabad are fixed, along with the charge for the distance covered. For a distance of $10 \mathrm{km}$, the charge paid is $₹220$. For a journey of $15 \mathrm{km}$, the charge paid is $₹310$. What are the fixed charges and charge per $\mathrm{km}$?

The larger of two supplementary angles exceeds the smaller by $18°$. Find the angles.

By comparing the ratios $\frac{a_1}{a_2}, \frac{b_1}{b_2}, \frac{c_1}{c_2}$, find out whether the lines represented by the following pair of linear equations intersect at a point, are parallel or are coincident.

$9x+3y+12=0$

$18x+6y+24=0$

If $6x+2y-9=0$ and $kx+y-7=0$ has no solution, then $k=$ _____

The pair of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ are consistent, then