Question

Which system of inequalities represents the graph?

Answer 1

The system which represent the graph is the number one, -y≤2x+8,
y-4x<-5 and 7y-7 ≤2x

Answer 2

Answer: The correct option is

`(2)~y+2x\leq-8,\\\\y+5>4x,\\\\-2x+7y\leq7.`

Step-by-step explanation: We are given to select the correct set of inequalities that represents the graph shown.

From the shaded region, let us consider a point (-6, -2).

The set of inequalities that will be satisfied by the point (x, y) = (-6, -2) is the required answer.

(1) The given set of inequalities are

`-y\leq2x+8,\\\\y-4x<-5,\\\\7y-7\leq2x.`

For (x, y) = (-6, -2), we have

`-y\leq2x+8\\\\\Rightarrow -(-2)\leq2(-6)+8\\\\\Rightarrow 2\leq-4,` which is not possible.

So, option (1) is NOT correct.

(2) The given set of inequalities are

`y+2x\leq-8,\\\\y+5>4x,\\\\-2x+7y\leq7.`

For (x, y) = (-6, -2), we have

`y+2x\leq-8\\\\\Rightarrow -2+2(-6)\leq-8\\\\\Rightarrow -14\leq-8,`true,

`y+5>4x\\\\\Rightarrow -2+5>4(-6)\\\\\Rightarrow 3>-24,` true,

`-2x+7y\leq7\\\\\Rightarrow -2(-6)+7(-2)\leq7\\\\\Rightarrow -2\leq7,` true.

Since all the three inequalities are satisfied by the point (-6, -2), so option (2) is CORRECT.

(3) The given set of inequalities are

`-y\geq2x+8,\\\\y-4x<-5,\\\\7y-7\geq2x.`

For (x, y) = (-6, -2), we have

`-y\geq2x+8\\\\\Rightarrow -(-2)\geq2(-6)+8\\\\\Rightarrow 2\geq-4,` true,

`y-4x<-5\\\\\Rightarrow -2-4(-6)<-5\\\\\Rightarrow 22<-5,` which is not possible.

So, option (3) is NOT correct.

(4) The given set of inequalities are

`y+2x\geq-8,\\\\y+5>4x,\\\\-2x+7y\geq7.`

For (x, y) = (-6, -2), we have

`-y+2x\geq-8\\\\\Rightarrow -(-2)+2(-6)\geq-8\\\\\Rightarrow -10\geq-8,` which is not possible.

So, option (4) is NOT correct.

Thus, option (2) is CORRECT.