CBSE Class 10 Mathematics Standard sample paper 2023-24: question 28(b)

Hints

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Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Let $\frac{1}{\sqrt{x}}=m$ and $\frac{1}{\sqrt{y}}=n$.

   ½ mark

2. The equations become:
   $$2m+3n=2\text{...(1)}$$
   $$4m-9n=-1\text{...(2)}$$

   ½ mark

3. Multiply (1) by 2: $4m+6n=4$. Subtract (2) from this: $15n=5$, so $n=\frac{1}{3}$.

   ½ mark

4. Substitute $n=\frac{1}{3}$ in (1): $2m+1=2$, so $2m=1$ and $m=\frac{1}{2}$.

   ½ mark

5. $\frac{1}{\sqrt{x}}=\frac{1}{2}\Rightarrow \sqrt{x}=2\Rightarrow x=4$

   $\frac{1}{\sqrt{y}}=\frac{1}{3}\Rightarrow \sqrt{y}=3\Rightarrow y=9$

   1 mark

Answer: $x=4$, $y=9$

Revise the chapter

• Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)
• Topic: Substitution Method