Question

Which of the following ordered pairs is a solution to the graph of the system of inequalities? Select all that apply(5.2)(-3,-4)(0.-3)(0.1)(-4,1)

Answer 1

For this type of question, we should draw a graph and find the area of the common solutions

`\begin{gathered} \because-2x-3\leq y \\ \therefore y\ge-2x-3 \end{gathered}`
`\begin{gathered} \because y-1<(1)/(2)x \\ \therefore y-1+1<(1)/(2)x+1 \\ \therefore y<(1)/(2)x+1 \end{gathered}`

Now we can draw the graphs of them

The red line represents the first inequality

The blue line represents the second inequality

The area of the two colors represents the area of the solutions,

Let us check the given points which one lies in this area

Point (5, -2) lies on the area of the solutions

∴ (5, -2) is a solution

Point (-3, -4) lies in the blue area only

∴ (-3, -4) not a solution

Point (0, -3) lies in the red line and the red line is solid, which means any point on it will be on the area of the solutions

∴ (0, -3) is a solution

Point (0, 1) lies in the blue line and the blue line is dashed, which means any point that lies on it not belong to the area of the solutions

∴ (0, 1) is not a solution

Point (-4, 1) lies on the area of the solutions

∴ (-4, 1) is a solution

The solutions are (5, -2), (0, -3), and (-4, 1)