`x lt 4 -2y`
`y le -2x +1`
Which of the following orfdered pairs satisfies both of the inequalities above ?

Options

A. `(-1,3)`
B. `(1,1)`
C. `(2,-3)`
D. `(4,4)`

Answer

C

Explanation

You could plot the two lines and identify the solution set on a graph, but testing the choices to see if they satisfy both inequalities is a more efficient approach, particularly since one inequality is "less than" and the other is "less than or equal to." If you take this approach, you don't even need to realrange the inequalities to isolate y on one side.
(A): Substtuting these values for x and y in `x lt 4 -2y` gives you `(-1) lt 4 - 2 (3),` whihc is `-1 lt =-2` (not a true statemetn). You don't need to evaluate the other inequality since this ordered pair is not in the solution set for `x lt 4 -2y.` Eliminate (A).
(B): Substituting these values for x and y in `x lt 4 -2y` gives you `(1) lt 4- 2 (1),` which is ` 1 lt 2.` The ordered pair is in the solution set for this inequality, so plug the values into `y le -1.` Thus, this ordered pair is not in the solution set for the second inequality. Eliminate (B).
(C ): Substituting these values for x and y in `x lt 4-2y` gives you `(2) lt 4 -2(-3),` whihc is `2 lt 10.` The ordered pair is in thte solution set for this inequality, so plug the values into `y le -2x + 1` to get `(-3)le -2 (2) +1.` which simplifies to `-3 le -3.` Since the sign for this inequality is "less than or equal to," this ordered pair is in the solution set. (C ) is correct.
(D): Since you already identified the correct choice, you do not need to check this pair.