Question

Consider the system of inequalities and its graph. y ≤ –0.75x y ≤ 3x – 2 In which section of the graph does the actual solution to the system lie?

A. 1

B. 2

C. 3

D. 4

Answer 1

4

Explanation:

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Answer 2

ANSWER

The actual solution lie in region 4.

EXPLANATION

The given system of inequalities are


`y \leqslant - 0.75x \: and \: y \leqslant 3x - 2`

Choose a point from each region and substitute in to the system of inequalities, the one that satisfies the system simultaneously is the actual solution.


Region 2: We test for

`(0,2)`
Thus,


`2 \leqslant - 0.75(0)\: and \: 2 \leqslant 3(0)- 2`


`2 \leqslant 0\: and \: 2 \leqslant- 2`
The above statement is false.


For region 1: We test for

`(-2,0)`


`0 \leqslant - 0.75( - 2)\: and \: 0 \leqslant 3( - 2) - 2`



`0 \leqslant 1.5\: and \: 0 \leqslant - 8`
The first statement is true but the second statement is false, so the whole thing is false.



For Region 3: We test

`(2,0)`


`0 \leqslant - 0.75(2) \: and \: 0 \leqslant 3(2)- 2`





`0 \leqslant - 1.5 \: and \: 0 \leqslant 4`

The first statement is false and the second is true so the whole statement is not true.



For region 4: We test


`(0,-4)`



`0 \leqslant - 0.75( - 4)\: and \: - 4 \leqslant 3( 0) - 2`


`0 \leqslant 3\: and \: - 4 \leqslant - 2`

Both statements are true, region 4 represents the actual solution to the system.