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(2,2) , (0,0), (5,3)

Step-by-step explanation:

To check which points are solution to the system of inequalities, substitute the value of those points in the two inequalities and make sure are both true.

y ≤ x

y > -x +1

Point (x=2, y=2)

2 ≤ 2 ✅

2 > -2 +1 ⇒ 2 > -1 ✅

Because both inequalities are true using the coordinates of this point then the point IS a solution to the system of inequalities.

Point (x= -2, y=2)

2 ≤ -2 ❌

We stop checking because we need both inequalities to work. This point IS NOT a solution.  

Point (x=0, y=0)

0 ≤ 0 ✅

0 > -0 +1 ⇒ 2 > 1 ✅

This point IS a solution.

Point (x=0, y=5)

5 ≤ 2 ❌

This point IS NOT a solution.

Point (x=2, y= -2)

-2 ≤ 2 ✅

-2 > -2 +1 ⇒ -2 > -1 ❌

This point IS NOT a solution.

Point (x=5, y=3)

3 ≤ 5 ✅

3 > -5 +1 ⇒ 3 > -4 ✅

This point IS a solution.

Point (x=4, y= -3)

-3 ≤ 4 ✅

-3 > -4 +1 ⇒ -3 > -3 ❌

This point IS NOT a solution.

Point (x=-2, y=-2)

-2 ≤ -2 ✅

-2 > - -2 +1 ⇒ -2 > 2+1 ⇒ -2 >3 ❌

This point IS NOT a solution.

step-by-step explanation:

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction