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Q3(ii):
Check which of the following are solutions of the equation $x - 2y = 4$ and which are not:
(ii) $(2, 0)$
Solution :
Given Variables & Initial Setup
We are tasked with determining whether the specific coordinate pair is a valid solution to the given linear equation in two variables.
- The Linear Equation: $x - 2y = 4$
- The Coordinate Pair to Test: $(2, 0)$
[Theoretical Foundation: A coordinate pair $(x, y)$ is considered a solution to a linear equation if and only if substituting the $x$ and $y$ values into the equation yields a true mathematical statement. This requires the Left-Hand Side (LHS) of the equation to perfectly equal the Right-Hand Side (RHS) after evaluation.]
Step 1: Isolate the Left-Hand Side (LHS) and Right-Hand Side (RHS)
From the given equation $x - 2y = 4$, we separate the expression into two distinct sides for independent evaluation:
- LHS: $x - 2y$
- RHS: $4$
Step 2: Substitution of the Coordinate Values
The given point is $(2, 0)$. In the Cartesian coordinate system, an ordered pair is formatted as $(x, y)$. Therefore, we extract the following values:
- $x = 2$
- $y = 0$
We substitute these specific values into the LHS expression:
$\text{LHS} = (2) - 2(0)$
Step 3: Algebraic Evaluation
Perform the arithmetic operations according to the standard order of operations (PEMDAS/BODMAS):
$\text{LHS} = 2 - 0$
$\text{LHS} = 2$
Step 4: Comparison and Logical Conclusion
Now, we compare the evaluated LHS with the constant RHS:
- $\text{LHS} = 2$
- $\text{RHS} = 4$
Since $2 \neq 4$, we conclude that $\text{LHS} \neq \text{RHS}$.
[Geometrical Interpretation: Because the equation is not satisfied, the point $(2, 0)$ does not lie on the straight line represented by the equation $x - 2y = 4$.]
Visual Verification: Graphical Representation
Below is the precise Cartesian plot of the line $x - 2y = 4$ alongside the tested point $(2, 0)$. Notice that the line intersects the x-axis at $(4, 0)$, leaving the point $(2, 0)$ distinctly off the line.
Final Solution: Since the substitution of $x = 2$ and $y = 0$ results in $2 \neq 4$, the coordinate pair $(2, 0)$ is NOT a solution to the equation $x - 2y = 4$.
More Questions from Class 9 Mathematics Linear Equations in Two Variables EXERCISE 4.2
- Q1: Which one of the following options is true, and why? $y = 3x + 5$ has
- Q2(i): Write four solutions for each of the following equations: (i) $2x + y = 7$
- Q2(ii): Write four solutions for each of the following equations: (ii) $\pi x + y = 9$
- Q2(iii): Write four solutions for each of the following equations: (iii) $x = 4y$
- Q3(i): Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (i) $(0, 2)$
- Q3(iii): Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (iii) $(4, 0)$
- Q3(iv): Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (iv) $(\sqrt{2}, 4\sqrt{2})$
- Q3(v): Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (v) $(1, 1)$
- Q4: Find the value of $k$, if $x = 2$, $y = 1$ is a solution of the equation $2x + 3y = k$.
CBSE Solutions for Class 9 Mathematics Linear Equations in Two Variables
Chapters in CBSE - Class 9 Mathematics
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