Question

Which of the following is a solution to the following system of inequalities?

solid line at y equals negative x plus one, dotted line at y equals two x plus 3, shaded above the first line and below the second line

(1, -1)

(-4, 0)

(3, -2)

(0, 3)

Answer 1

Option D: $(0,3)$ is the solution to the inequalities.

Explanation:

From the given graph, we can see that the equation of the inequalities are

$y>-x+1$ and $y\leq 2 x+3$

To determine the coordinate that satisfies the inequality, let us substitute the coordinates in both of the inequalities $y>-x+1$ and $y<2 x+3$

Thus, we have,

Option A: $(1,-1)$

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$, we get,

$y>-x+1\implies-1>0$ is not true.

$y\leq 2 x+3 \implies -1\leq 5$ is true.

Since, only one equation satisfies the condition, the coordinate $(1,-1)$ is not a solution.

Hence, Option A is not the correct answer.

Option B: $(-4,0)$

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$, we get,

$y>-x+1\implies0>5$ is not true.

$y\leq 2 x+3 \implies 0\leq -5$ is not true.

Since, both the equations does not satisfy the condition, the coordinate $(-4,0)$ is not a solution.

Hence, Option B is not the correct answer.

Option C: $(3,-2)$

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$, we get,

$y>-x+1\implies-2>-2$ is not true.

$y\leq 2 x+3 \implies -2\leq 9$ is true.

Since, only one equation satisfies the condition, the coordinate $(3,-2)$ is not a solution.

Hence, Option C is not the correct answer.

Option D: $(0,3)$

Substituting the coordinates in $y>-x+1$ and $y\leq 2 x+3$, we get,

$y>-x+1\implies3>1$ is true.

$y\leq 2 x+3 \implies 3\leq 3$ is true.

Since, both equation satisfies the condition, the coordinate $(0,3)$ is a solution.

Hence, Option D is the correct answer.