Question

Choose the graph below that represents the following system of inequalities:

y ≥ −3x + 1

y ≤ 1 over 2x + 3


A)Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.
B)Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.
C)Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded below the line.
D)Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded below the line.

Answer 1

Answer: The correct answer is Y

Answer 2

we have

`y \geq -3x + 1 \\ \\ y \leq (1)/(2) x+3`

using a graph tool

see the attached figure

The solution of the system is the shaded area

we know that

`y \geq -3x + 1`

The line is solid

The line passes through points
`(0,1)` and
`(1,-2)` and is shaded above the line.

`y \leq (1)/(2) x+3`

The line is solid

The line passes through points
`(-2,2)` and
`(0,3)` and is shaded below the line

The two lines intersect at one point

therefore

the answer is the option

B) Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.