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# 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,

$x$ | $y=3x+5$ |

2 | $y=3(2)+5=6+5=11$ |

3 | $y=3(3)+5=9+5=14$ |

4 | $y=3(4)+5=12+5=17$ |

..... | ....... |

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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