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Question 1: Write the general form of a linear equation in two variables.
Solution: The general form is $ax + by + c = 0$, where $a, b, c$ are real numbers and $a$ and $b$ are not both zero.
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Question 2: How many solutions does a linear equation in two variables have?
Solution: It has infinitely many solutions.
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Question 3: Write the equation $2x = 5$ in the standard form $ax + by + c = 0$.
Solution: $2x + 0y - 5 = 0$. Here $a=2, b=0, c=-5$.
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Question 4: What is the equation of the x-axis?
Solution: The equation of the x-axis is $y = 0$.
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Question 5: Check whether $x=2, y=1$ is a solution of the equation $2x + 3y = 7$.
Solution: LHS = $2(2) + 3(1) = 4 + 3 = 7$. RHS = 7. Since LHS = RHS, it is a solution.
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Question 6: The graph of the equation $y = mx$ passes through which specific point?
Solution: It always passes through the Origin $(0, 0)$.
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Question 7: Express $y$ in terms of $x$ for the equation $2x - y = 4$.
Solution: $-y = 4 - 2x \Rightarrow y = 2x - 4$.
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Question 8: Any point on the y-axis is of the form?
Solution: $(0, y)$.
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Question 9: What is the degree of a linear equation in two variables?
Solution: The degree is 1.
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Question 10: The graph of $x = 5$ is a line parallel to which axis?
Solution: It is parallel to the y-axis.