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# Ex.4.2 Q1 Linear Equations in Two Variables Solution - NCERT Maths Class 9

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## Question

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

Video Solution
Linear Equations In Two Variables
Ex 4.2 | Question 1

## Text Solution

What is known?
Linear equation \begin{align} y = 3x + 5\end{align}

What is Unknown?
Number of solutions of the given equation.

Reasoning:
We can check number of solution by putting different values of $$x$$ and get different values of $$y$$.

Steps:

We know that

• $$y = 3x + 5$$ is a linear equation in two variables in the form of $$ax + by + c = 0$$
• For $$x = 0, y = 0 + 5 = 5$$          Therefore, $$(0, 5)$$ is one solution.
• For $$x = 1, y = 3×1 + 5 = 8$$      Therefore, $$(1, 8)$$ is another solution.
• For $$y = 0, 3x + 5 = 0, x = - 5/3$$   Therefore, $$(- 5/3 , 0)$$ is another solution .

Clearly, for different values of $$x$$, we get various values for $$y$$.

Thus, any value substituted for $$x$$ in the given equation will constitute another solution for the given equation.

So, there is no end to the number of different solutions obtained on substituting real values for $$x$$ in the given linear equation. Therefore, a linear equation in two variables has infinitely many solutions.

Hence (iii) is the correct answer

Video Solution
Linear Equations In Two Variables
Ex 4.2 | Question 1

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