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# $$y < x - a$$ $$y > x + b$$In the xy-plane, if (0, 0) is a solution to t...

### Question

$$y < x - a$$
$$y > x + b$$

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?

### Options

A)
a > b
B)
b > a
C)
|a| > |b|
D)
a = -b

Choice A is correct. 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 $$a = -b$$ doesn't have to be true;  for example, (0,0) is a solution to the system of inequalities if $$a = 1$$ and $$b = -2$$.