Question

Select the point that is a solution to the system of inequalities. Y ≤ x+1,Y ≤ x^2-3x

Answer 1

Point D(0,-2) is a solution of the system of inequalities

Step-by-step explanation:

In order to check if the points are solution of the system of inequalities, we just need to plug the numbers into the inequalities and see if they are verified.

The two inequalities are:

$y\leq x+1\\y\leq x^2-3x$

The first point is:

A (1,0), so x = 1 and y = 0

Substituting into the two equations:

$0\leq 1+1\rightarrow 0\leq 2\\0\leq 1^2 -3\cdot 1 \rightarrow 0\leq -2$

We see that the 2nd equation is not verified, so this point is NOT a solution.

The second point is:

B (2,4), so x = 2 and y = 4

Substituting into the two equations:

$4\leq 2+1\rightarrow 4\leq 3\\4\leq 2^2 -3\cdot 2 \rightarrow 4\leq 1$

None of the two equations is verified, so this point is NOT a solution.

The 3rd point is:

C (-1,2), so x = -1 and y = 2

Substituting into the two equations:

$2\leq -1+1\rightarrow 2\leq 0\\2\leq (-1)^2 -3\cdot (-1) \rightarrow 2\leq 4$

We see that the 1st equation is not verified, so this point is NOT a solution.

The 4th point is:

D (0,-2), so x = 0 and y = -2

Substituting into the two equations:

$-2\leq 0+1\rightarrow -2\leq 1\\-2\leq 0^2 -3\cdot 0 \rightarrow -2\leq 0$

Both equations are verified, so this point IS a solution.

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