CBSE Class 10 Mathematics — If the system of equations $2x

Q: If the system of equations $2x + 3y = 7$ and $2ax + (a + b)y = 28$ has infinitely many solutions, then:

For infinitely many solutions: $\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$. $\frac{2}{2a} = \frac{3}{a+b} = \frac{7}{28}$.\nFrom $\frac{2}{2a} = \frac{7}{28} = \frac{1}{4} \implies \frac{1}{a} = \frac{1}{4} \implies a = 4$.\nFrom $\frac{3}{a+b} = \frac{1}{4} \implies a + b = 12 \implies 4 + b = 12 \implies b = 8$.\nThus, $b = 2a$ ($8 = 2 \times 4$).

CBSE · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesIf the system of equations $2x + 3y = 7$ and $2ax + (a + b)y = 28$ has infinitely many solutions, then:

Step-by-Step Solution

For infinitely many solutions: $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$. $\frac{2}{2a} = \frac{3}{a+b} = \frac{7}{28}$.\nFrom $\frac{2}{2a} = \frac{7}{28} = \frac{1}{4} \implies \frac{1}{a} = \frac{1}{4} \implies a = 4$.\nFrom $\frac{3}{a+b} = \frac{1}{4} \implies a + b = 12 \implies 4 + b = 12 \implies b = 8$.\nThus, $b = 2a$ ($8 = 2 \times 4$).

Detailed Options Breakdown

Option : $a = 2b$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.

Option 1: $b = 2a$ (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 2: $a + 2b = 0$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.

Option 3: $2a + b = 0$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.

💡 Study Guide: This question tests core syllabus concepts from Pair of Linear Equations in Two Variables. For formulas, key summaries, and mock exam reference guides, read the full Pair of Linear Equations in Two Variables Revision Notes.

✓

Verified by Academic Committee