225k views
5 votes
Here is a graph of the equation 6x + 2y = -8.Check if each of these points is a solution to the inequality 6x + 2y ≤ -8:(-2, 2) (4, -2) (0, 0) (-4, -4)

Here is a graph of the equation 6x + 2y = -8.Check if each of these points is a solution-example-1
User HussoM
by
7.5k points

1 Answer

7 votes

Answer:

(-2, 2) & (-4, -4)

Step-by-step explanation:

We are given the graph of the equation 6x + 2y = -8

We are to check if the following points are a solution to the inequality 6x + 2y ≤ -8

We will do this using 2 methods:

I. Substitution method

II. Graphical method

I. For the substitution method, we will substitute the variables into the inequality as shown below:


\begin{gathered} 6x+2y\le-8 \\ \\ \mleft(x,y\mright)=\mleft(-2,2\mright) \\ 6\mleft(-2\mright)+2(2)\le-8 \\ -12+4\le-8 \\ -8\le-8----------(TRUE) \\ \\ (x,y)=(4,-2) \\ 6(4)+2(-2)\le-8 \\ 24-4\le-8 \\ 20\le-8----------(FALSE) \\ \\ (x,y)=(0,0) \\ 6(0)+2(0)\le-8 \\ 0+0\le-8 \\ 0\le-8----------(FALSE) \\ \\ (x,y)=(-4,-4) \\ 6(-4)+2(-4)\le-8 \\ -24-8\le-8 \\ -32\le-8--------(TRUE) \end{gathered}

II. For the graphical method, we have:

The solution is given by any point that falls within the shaded portion of the graph

Therefore, the points (-2, 2) & (-4, -4) is a solution to the inequality 6x + 2y ≤ -8

Here is a graph of the equation 6x + 2y = -8.Check if each of these points is a solution-example-1
User Flies
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories