Question

A machine takes 2 litres of petrol to start and then 3 litres per hour while running. If the equation thus formed is of the form of ax+by+c=0. What is the value of a when a linear equation is written as $ax+by+2=0$ .

Answer 1

Hint: Let the total amount of petrol consumed be y litres and the time for which the machine has been running be x. Now use the condition given in the question to get the relation between x and y and reach the answer. You need to report the answer by using the equation in the form where c=2.

Complete step-by-step answer:
Before starting with the solution, let us discuss the significance of linear equations in two variables. Linear equations in two variables represent the equation of a line on the Cartesian plane.
To start the solution to the above question, we let the total amount of petrol consumed be y litres and the time for which the machine has been running be x.
Now it is given in the question that the machine takes 2 litres of petrol to start and then 3 litres per hour while running, so the total amount of fuel used is the sum of the amount required for starting and the amount used for running. The amount used for running the machine for x hours is 3x. So, if we represent this mathematically, we get
$y=3x+2$
$\Rightarrow 0=3x+2-y$
$\Rightarrow 3x-y+2=0$
Therefore, the answer to the above question is 3.

Note:Be careful with the signs and calculations as in such questions, the possibility of making a mistake is either of the sign or a calculation error. Also, it would leave you a different answer if you let the total amount consumed to be y and time to be t, but generally we take the most significant output, for this case the amount of fuel consumed, to be y and report the answers accordingly.