Easy
State whether the following statement is true or false:
An equation in two variables has a unique solution.
An equation in two variables has a unique solution.
(B) The statement is False.
$A$ linear equation in two variables,typically represented as $ax + by + c = 0$,where $a, b,$ and $c$ are real numbers and $a, b \neq 0$,has infinitely many solutions.
For any value assigned to one variable,there exists a corresponding value for the other variable that satisfies the equation. Therefore,it does not have a unique solution.
$A$ linear equation in two variables,typically represented as $ax + by + c = 0$,where $a, b,$ and $c$ are real numbers and $a, b \neq 0$,has infinitely many solutions.
For any value assigned to one variable,there exists a corresponding value for the other variable that satisfies the equation. Therefore,it does not have a unique solution.
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The linear equation $2x - 5y = 7$ has:
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View SolutionWrite whether the following statements are True or False? Justify your answers.
$(i)$ $ax + by + c = 0$,where $a, b$ and $c$ are real numbers,is a linear equation in two variables.
$(ii)$ $A$ linear equation $2x + 3y = 5$ has a unique solution.
$(iii)$ All the points $(2, 0), (-3, 0), (4, 2)$ and $(0, 5)$ lie on the $x$-axis.
$(i)$ $ax + by + c = 0$,where $a, b$ and $c$ are real numbers,is a linear equation in two variables.
$(ii)$ $A$ linear equation $2x + 3y = 5$ has a unique solution.
$(iii)$ All the points $(2, 0), (-3, 0), (4, 2)$ and $(0, 5)$ lie on the $x$-axis.
Easy
View SolutionThe autorickshaw fare in a city is as follows: For the first kilometre,the fare is ₹ $10$,and for the subsequent distance,it is ₹ $3$ per $km$. Taking the distance covered as $x$ $km$ and the total fare as ₹ $y$,write a linear equation for this information and draw its graph. Find the total fare for a journey of $4$ kilometres from the graph.
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View SolutionIf $(2, -3)$ is a solution of the equation $3x + ky = 18$,find the value of $k$.
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View SolutionExpress the following linear equation in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in each case: $6x - 5y = 4.2\overline{7}$
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