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Algebra / Linear inequalities in one or two variables Difficulty: Medium

$y < x$

$x less than 22$

For which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the given system of inequalities?

$x$	$y$
$19$	$18$
$20$	$19$
$21$	$20$

$x$	$y$
$19$	$20$
$20$	$21$
$21$	$22$

$x$	$y$
$23$	$22$
$24$	$23$
$25$	$24$

$x$	$y$
$23$	$24$
$24$	$25$
$25$	$26$

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Explanation

Choice A is correct. The inequality $y < x$ indicates that for any solution to the given system of inequalities, the value of $x$ must be greater than the corresponding value of $y$ . The inequality $x less than 22$ indicates that for any solution to the given system of inequalities, the value of $x$ must be less than $22$ . Of the given choices, only choice A contains values of $x$ that are each greater than the corresponding value of $y$ and less than $22$ . Therefore, for choice A, all the values of $x$ and their corresponding values of $y$ are solutions to the given system of inequalities.

Choice B is incorrect. The values in this table aren’t solutions to the inequality $y < x$ .

Choice C is incorrect. The values in this table aren’t solutions to the inequality $x less than 22$ .

Choice D is incorrect. The values in this table aren’t solutions to the inequality $y < x$ or the inequality $x less than 22$ .