QJEEM13Maf4c8: JEE Main 2013 Mathematics - Class 12 JEEM13Maf4c8 Solution: The number of values of k , for which the system of equations : …

Question

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The number of values of

k

, for which the system of equations :

</mo></mrow><mtable rowspacing="4pt" columnspacing="1em"><mtr><mtd><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>+</mo><mn>1</mn></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>x</mi><mo>+</mo><mn>8</mn><mi>y</mi><mo>=</mo><mn>4</mn><mi>k</mi></mrow></mtd></mtr><mtr><mtd><mrow data-mjx-texclass="ORD"><mi>k</mi><mi>x</mi><mo>+</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mi>k</mi><mo>+</mo><mn>3</mn></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>y</mi><mo>=</mo><mn>3</mn><mi>k</mi><mo>−</mo><mn>1</mn></mrow></mtd></mtr></mtable></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container>

Accepted Answer

From the given system, we have

\frac{k + 1}{k} = \frac{8}{k + 3} \neq \frac{4 k}{3 k - 1}

( as System has no solution)

\Rightarrow k^{2} + 4 k + 3 = 8 k

\Rightarrow k = 1, 3

If

k = 1

then

\frac{8}{1 + 3} \neq \frac{4.1}{2}

which is false

And if

k = 3

Then

\frac{8}{6} \neq \frac{4.3}{9 - 1}

which is true, therefore

k = 3

Hence for only one value of

k .

System has no solution.

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