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4. Linear Equations in Two Variables
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Write whether the following statements are True or False? Justify your answers.
$(i)$ $a x+b y+c=0,$ where $a, b$ and $c$ are real numbers, is a linear equation in two variables.
$(ii)$ A linear equation $2 x+3 y=5$ has a unique solution.
$(iii)$ All the points $(2,0),(-3,0),(4,2)$ and $(0,5)$ lie on the $x$ -axis.
Option A
Option B
Option C
Option D
Solution
$(i)$ False, because $a x+b y+c=0$ is a linear equation in two variables if both $a$ and $b$ are non-zero.
$(ii)$ False, because a linear equation in two variables has infinitely many solutions.
$(iii)$ False, the points $(2,0),(-3,0)$ lie on the $x$ -axis. The point $(4,2)$ lies in the first quadrant. The point $(0,5)$ lies on the $y$ -axis.
Standard 9
Mathematics
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