Question

Given the system of inequalities, choose the answer that represents a solution:

y> 6x - 3
4
y≤-3x+4
(0,0)
(5,0)
(0,6)
(0, -10)

Answer 1

Correct choices are:

Choice 1: (-5, 5)
Choice 4: (-10, -3)
Choice 5: (0, -2)

Explanation:

Note:

The inequalities you have posted and the screenshot are different. I a going with the screenshot

Plug in each of the x, y values in each answer choice into each of the two inequalities

If one pair of (x, y) values violates even one inequality, it does not satisfy

(x, y) values in both inequalities must be satisfied

System of inequalities

`y > x - 6\quad\quad(1)\\ y < -2x \quad\quad(2)`

You have chosen two of the correct answers:
First option (-5, 5)

4th option: (-10, -3)

Plug in each of the values and see that it is consistent

I will provide explanation for two of them since you have already got two right

Choice 2 : (0, 0)
Substituting x = 0, y = 0 gives
For (1): 0 > 0 - 6==> 0 > - 6 True
For (2); 0 < -2(0) ==> 0 < 0 False
Choice 2 → (0, 0) does not satisfy inequality (2)

Choice 5: (0, - 2)
Substituting x = 0, y = -2 gives
For (1): y > x - 6
==> -2 > 0 - 6 ==> -2 > -6 True

For (2): y < -2x
==> -2 < -2(0) ==> -2 < 0 True
Choice 5, (0, -2) satisfies both inequalities

Not of the other choices result in a consistent system