Given, $y < - x + a$ and $y > x + b$
In the $x y$ -plane, if $(0, 0)$ is a solution to the system of inequalities above, which of the following relationship between $a$ and $b$ must be true?

a > b

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b > a

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| a | > | b |

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a = - b

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Solution

The correct option is A $a > b$
Given, $y < - x + a$ and $y > x + b$
As given, $(0, 0)$ is a solution to the above inequalities.
$\Rightarrow 0 < 0 + a$ and $0 > 0 + b$
$\Rightarrow a > 0$ and $b < 0$
Thus, we can conclude from the above inequalities that $a$ is a positive number and $b$ is a negative quantity.
Therefore, it can be surely said that $a > b$ .

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Given, y<−x+a and y>x+bIn the xy-plane, if (0,0) is a solution to the system of inequalities above, which of the following relationship between a and b must be true?

The correct option is A a>bGiven, y<−x+a and y>x+bAs given, (0,0) is a solution to the above inequalities.⇒0<0+a and 0>0+b⇒a>0 and b<0Thus, we can conclude from the above inequalities that a is a positive number and b is a negative quantity.Therefore, it can be surely said that a>b.

Given, $y < - x + a$ and $y > x + b$
In the $x y$ -plane, if $(0, 0)$ is a solution to the system of inequalities above, which of the following relationship between $a$ and $b$ must be true?