SATMathematics Practice Test 1

Question : 38 of 58

Marks: +1, -0

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

$a > b$
$b > a$
$|a| > |b|$
$a=-b$

Validate

Solution:

Since (0, 0) is a solution to the system of inequalities,substituting 0 for x and 0 for y in the given system must result in two true inequalities. After this substitution,

y < −x+a

becomes

0 < a

, and

y > x+b

becomes

0 > b

. Hence, a is positive and b is negative. Therefore,

a > b

.
Choice B is incorrect because b > a cannot be true if b is negative and a is positive. Choice C is incorrect because it is possible to find an example where

(0, 0)

is a solution to the system, but

|a| < |b|

; for example, if

a=6

and

b=−7

. Choice D is incorrect because the equation a = −b could be true, butdoesn’t have to be true; for example, if

a=1

and

b=−2

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