P(x, y) is a point on the Cartesian plane such that 4x+7<-3 and 5-3y_>11. In which quadrant does the point P lie? Show your working​

3rd quadrant.

Step-by-step explanation:

We know that

4x + 7 < -3

5 - 3*y ≥ 11

We should isolate both of the variables in these inequalities:

for the first one we get:

4x + 7 < - 3

4x < -3 - 7

4x < -10

x < -10/4

So x is smaller than a negative number, then we know that x is negative, from this we already know that the point will be on quadrants 2 or 3.

For the other inequality we get:

5 - 3*y ≥ 11

5 - 11 ≥ 3y

-6 ≥ 3y

-6/3 ≥ y

-2 ≥  y

So we can see that y is equal to or smaller than a negative number, then y is a negative number.

So both values, x and y, are negatives.

This means that the point P(x, y) is in the 3rd quadrant.

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step-by-step explanation: