Question

Which ordered pairs make both inequalities true? Check all that apply. y < 5 x + 2 y > 1/2 x + 1

(–3, 2)

(–1, 3)

(0, 2)

(1, 2)
(2, –1)
(2, 2)

Answer 1

for (-3, 2): 2 > 5(-3) + 2; 2 > -15 + 2; 2 > -13 (i.e. not correct)
for (-1, 3): 2 > 5(-1) + 2; 2 > -5 + 2; 2 > -3 (i.e. not correct)
for (0, 2): 2 = 5(0) + 2; 2 = 0 + 2; 2 = 2 (i.e. not correct)
for (1, 2): 2 < 5(1) + 2; 2 < 5 + 2; 2 < 7 (i.e. correct): 2 > 1/2(1) + 1; 2 > 1/2 + 1; 2 > 3/2 (i.e. correct)
for (2, -1): -1 < 5(2) + 2; -1 < 10 + 2; -1 < 12 (i.e. correct): -1 < 1/2(2) + 1; -1 < 1 + 1; -1 < 2 (i.e. not correct)
for (2, 2): 2 < 5(2) + 2; 2 < 10 + 2; 2 < 12 (i.e. correct): 2 = 1/2(2) + 1; 2 = 1 + 1; 2 = 2 (i.e. not correct)

Therefore, both ineaqualities are tru for only the ordered pair (1, 2)