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Byju's Answer

Standard XII

Mathematics

Eccentricity

If 0,0 is t...

Question

If $(0, 0)$ is the solution for the system of inequalities $y < x + k_{1}$ , $y < 2 x + k_{2}$ .Which of the following conclusions about $k_{1}$ and $k_{2}$ must be true?

k_{1} < k_{2}

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k_{2} < k_{1}

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| k_{1} | < | k_{2} |

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k_{1} = - k_{2}

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Solution

The correct option is B $k_{1} < k_{2}$
Given, $y < x + k_{1}$ and $y > 2 x + k_{2}$
Then
$2 x + k_{2} > x + k_{1}$
Put the value $(0, 0)$ in above inequality, we get
$2 \times 0 + k_{2} > 1 \times 0 + k_{1}$
$\Rightarrow k_{2} > k_{1}$

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If (0,0) is the solution for the system of inequalities y<x+k1, y<2x+k2.Which of the following conclusions about k1 and k2 must be true?

The correct option is B k1<k2Given, y<x+k1 and y>2x+k2Then 2x+k2>x+k1Put the value (0,0) in above inequality, we get2×0+k2>1×0+k1⇒k2>k1

If $(0, 0)$ is the solution for the system of inequalities $y < x + k_{1}$ , $y < 2 x + k_{2}$ .Which of the following conclusions about $k_{1}$ and $k_{2}$ must be true?

The correct option is B $k_{1} < k_{2}$
Given, $y < x + k_{1}$ and $y > 2 x + k_{2}$
Then
$2 x + k_{2} > x + k_{1}$
Put the value $(0, 0)$ in above inequality, we get
$2 \times 0 + k_{2} > 1 \times 0 + k_{1}$
$\Rightarrow k_{2} > k_{1}$