Q3(ii):

Check which of the following are solutions of the equation $x - 2y = 4$ and which are not: (ii) $(2, 0)$

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 $x - 2y = 4$.