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