Karnataka Board Solutions for Chapter: Solved Examples, Exercise 3: exercise 3

Use elimination method to find all possible solutions of the following pair of linear equations :

$2x+3y=8 \left(1\right)$

$4x+6y=7 \left(2\right)$

The sum of a two-digit number and the number obtained by reversing the digits is $66$. If the digits of the number differ by $2$, find the number. How many such numbers are there?

From a bus stand in Bangalore, if we buy $2$ tickets to Malleswaram and $3$ tickets to Yeshwanthpur, the total cost is $₹46$; but if we buy $3$ tickets to Malleswaram and $5$ tickets to Yeshwanthpur the total cost is $₹74$. Find the fares from the bus stand to Malleswaram, and to Yeshwanthpur.

For which values of $p$ does the pair of equations given below has unique solution?

$4x+py+8=0$

$2x+2y+2=0$

For what values of $k$ will the following pair of linear equations have infinitely many solutions?

$kx+3y-\left(k-3\right)=0$

$12x+ky-k=0$

Solve the pair of equations:

$\frac{2}{x}+\frac{3}{y}=13$

$\frac{5}{x}-\frac{4}{y}=-2$

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

$\frac{5}{x-1}+\frac{1}{y-2}=2$

$\frac{6}{x-1}-\frac{3}{y-2}=1$

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 $55 \mathrm{km}$ down-stream. Determine the speed of the stream and that of the boat in still water.