The figure above shows the solution set for this system of inequalities:
`{{:(x lt 3/5 x -2),(y le -4/3 x +5):}`
Which of the following is NOT is solution to this system ?

Options

A. `(-1,-4)`
B. `(1,-1)`
C. `(4,-1)`
D. `(6,-3)`

Answer

B

Explanation

The intersection (overlap) of the two shaded regions is the solution to the system of inequalities. Check each point to see whether it lies in the region where the shading overalaps. Be careful-you are looking for the point that is not a solution to the system. Choice (A) and (C )lie in the overlap, so you can eliminte them. Choice (D), which is the point `(6, -3),` lies on a boundary line, and because the line is solid, the point is included in the solution region. The only point that does not lie within the overlap must be (B). To check this, plug `(1, -1)` into the first inequality:
` y le 3/5 x-`
`-1 lt 3/5 (1)-2` ltbr. `-1 cancel(lt) - 7/5`
Because -1 is not less than -07/5,(B) is correct.