Question

y < 3x + 4
y < 5x + 2
which of the following ordered pairs (x, y) satisfies the system of inequalities?
choose 1 answer:
a (-1, 0)
b (1, 7)
c (2, 11)
d (3, -4)

Explanation:

Step1: Test option A (-1,0)

For $y < 3x + 4$, substitute $x=-1$ and $y = 0$: $0<3\times(-1)+4=1$ (true). For $y < 5x+2$, substitute $x=-1$ and $y = 0$: $0<5\times(-1)+2=-3$ (false).

Step2: Test option B (1,7)

For $y < 3x + 4$, substitute $x = 1$ and $y=7$: $7<3\times1 + 4=7$ (false).

Step3: Test option C (2,11)

For $y < 3x + 4$, substitute $x = 2$ and $y = 11$: $11<3\times2+4=10$ (false).

Step4: Test option D (3,-4)

For $y < 3x + 4$, substitute $x = 3$ and $y=-4$: $-4<3\times3+4=13$ (true). For $y < 5x+2$, substitute $x = 3$ and $y=-4$: $-4<5\times3+2=17$ (true).

Answer:

D. $(3,-4)$