Question

4.06 Question 9

Answer 1

Answer:

we have

$\begin{gathered} y \geq -3x + 1 \\ \\ y \leq \frac{1}{2} x+3 \end{gathered}$

using a graph tool

see the attached figure

The solution of the system is the shaded area

we know that

The line is solid

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

$y \leq \frac{1}{2} x+3$

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.

${\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt}{\red{\rule{100pt}{5pt}{\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt} }}}}}}}}}}$${\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt}{\red{\rule{100pt}{5pt}{\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt} }}}}}}}}}}$${\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt}{\red{\rule{100pt}{5pt}{\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt} }}}}}}}}}}$

Answer 2

Answer: B. Graph of 2 lines that intersect at one point. Both lines are solid. One line passes through (-2,2) and (0,3) and is shaded below the line.

y < = 1/2x + 3...(-2,2)                y < = 1/2x + 3....(0,3)

2 < = 1/2(-2) + 3                        3 < = 1/2(0) + 3

2 < = -1 + 3                                3 < = 0 + 3

2 < = 2 (correct)                        3 < = 3 (correct)

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

y > = -3x + 1...(0,1)            y > = -3x + 1...(1,-2)

1 > = -3(0) + 1                   -2 > = -3(1) + 1

1 > = 0 + 1                         -2 > = -3 + 1

1 > = 1 (correct)                 -2 > = -2 (correct)