Question

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)

Answer 1

(-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