Q. 14.0( 208 Votes )

# Which one of the following options is true, and why?

y = 3x + 5 has

(i) A unique solution,

(ii) Only two solutions,

(iii) Infinitely many solutions

Answer :

Equation y = 3x + 5 is a linear equation in two variables.

This means that we can put any value of x and in return, we will get some other value of y.

For example, at x = 0, y = 3 x 0 + 5, y = 5

at x = 1000, y = 3 x 1000 + 5, y = 3005

we can put infinitely many values of x and we will get infinitely many solutions for y.

Thus there are infinite solutions for the equation.

Graphically:

When plotted graphically, it will give a straight line extending to infinity and thus will give infinite solutions.

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