Let us consider the equation 2x + 3y = 12. Here, x = 3 and y = 2 is a solution of the linear equation. This solution is written as an ordered pair (3, 2), first writing the value for x and then the value for y. So there is no end to different solutions of a linear equation in two variables. That is, a linear equation in two variables has infinitely many solutions.
Remark : Note that an easy way of getting a solution is to take x = 0 and get the corresponding value of y. Similarly, we can put y = 0 and obtain the corresponding value of x.
Shaalaa.com | Solution of a Linear Equation
A lending library has a fixed charge for the first three days and an additional charge for each
day thereafter. Aarushi paid Rs 27 for a book kept for seven days. If fixed charges are Rs 𝑥
and per day charges are Rs y. Write the linear equation representing the above information.
A three-wheeler scooter charges Rs 15 for first kilometer and Rs 8 each for every subsequent
kilometer. For a distance of x km, an amount of Rs y is paid. Write the linear equation
representing the above information.
Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equation :
−4x + 3y = 12