Which one of the following options is true, and why? $ y=3 x+5 $ has
(i) a unique solution,
(ii) only two solutions,
(iii) infinitely many solutions.

To do:

We have to find which one of the given options is true and why.

Solution:

Let us substitute $x=0$ in the given equation $y= 3x+5$

We get,

$y=3(0)+5$

$y=0+5$

$y=5$

If we substitute $x=1$

We get,

 $y=3(1)+5$

$y=3+5$

$y=8$

In the similar way,

If we substitute $x=2,3,4,5.......$

We get,

Therefore,

From the table we can observe that for infinite values of x, we can get infinite values of y.

Hence, $y=3x+5$ has infinitely many solutions.

Therefore,

From the given options, (iii) is True. 

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Updated on: 10-Oct-2022

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