The path of a train A is given by the equation  $x+2y-4=0$ and the path of another train B is given by the equation  $2x+4y-12=0$ .  Will the paths cross ?  Solve by the method of substitution.

The sum of a two digit number and the number formed by interchanging its digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the first number. Find the first number.

For what values of k will the following pair of linear equations have infinitely many solutions ?                                                                      $kx+3y-\left(k-3\right)=0$  and  $12x+ky-k=0$  

What is the solution to a system of equations?

There are several human beings and several dogs in a room. One tenth of the humans have lost a leg. The total numbers of feet are 77, then the number of dogs is

Ganesh has to pay Rs. 482 for 19 apples and 11 guavas. If he would have exchanged the number of apples and guavas purchased, then he would have paid Rs.64 less. Find how much more amount he has to pay to purchase 1 apple than 1 guava

The pair of equations  $ax+2y=7$  and  $3x+by=16$  represent parallel lines if :

Solution of the system of equations  $\sqrt{2}x-\sqrt{5}y=0$  and  $\sqrt{5}x+\sqrt{2}y=0$  is

The pair of equations  $x=2$  and  $y=3$  graphically represents lines which are :

If a pair of linear equations is consistent, then the lines will be

A fraction becomes  $\frac{6}{5}$ , if 1 is added to each of the numerator and denominator. However, if we subtract 5 from each, the fraction becomes  $\frac{3}{2}$ . Then the fraction is :