`y gt 2x -1`
`2x gt 5`
Which of the following consists of the y-coordinates of all the points that satisfy the system of inequalities above?

Options

A. `y gt 6`
B. `y gt 4`
C. `y gt 5/2`
D. `y gt 3/2`

Answer

B

Explanation

Subtracting the same number from each side of an inequality gives an equivalent inequality. Hence, subtracting 1 from each side of the inequality 2x gt 5 gives 2x − 1 gt 4. So the given system of inequalities is equivalent to the system of inequalities y gt 2x − 1 and 2x − 1 gt 4, which can be rewritten as y gt 2x − 1 gt 4. Using the transitive property of inequalities, it follows that y gt 4.
Choice A is incorrect because there are points with a y-coordinate less than 6 that satisfy the given system of inequalities. For example, (3, 5.5) satisfies both inequalities. Choice C is incorrect. This may result from solving the inequality 2x gt 5 for x, then replacing x with y. Choice D is incorrect because this inequality allows y-values that are not the y-coordinate of any point that satisfies both inequalities. For example, y = 2 is contained in the set `y gt 3/2` , however, if 2 is substituted into the first inequality for y, the result is `x lt 3/2`. This cannot be true because the second inequality gives `x gt 5/2` .