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Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10

Question:

Determine, without solving completely, whether the pair of equations $2x-3y=8$ and $4x-6y=9$ is consistent or inconsistent, and describe how the lines would appear if graphed.

Step-by-Step Solution

Key Concept: Compare all three ratios of coefficients.
$\dfrac{a_1}{a_2}=\dfrac{2}{4}=\dfrac12,\ \dfrac{b_1}{b_2}=\dfrac{-3}{-6}=\dfrac12,\ \dfrac{c_1}{c_2}=\dfrac{8}{9}$. [1.0 Mark]

Since $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}
eq\dfrac{c_1}{c_2}$, the pair is inconsistent (has no solution). [1.0 Mark]

Graphically, this means the two lines are parallel to each other but do not coincide — they never meet. [1.0 Mark]

Correct Answer:
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