Select all the points that are solutions to the system of linear inequalities that is listed below 10x + 4y < 12
8x - 3y > 20
. (3, -8) (2, 5) (-5, 1) (10, 3) (2, -10)

(3,-8)

(2,-10)

Step-by-step explanation:

we have

----> inequality A

----> inequality B

we know that

If a point is a solution of the system of inequalities, then the point must satisfy both inequalities (makes true both inequalities)

Verify  all the points

Substitute the value of x and the value of y of each point in both inequalities  

Case 1) point (3,-8)    

For x=3, y=-8

inequality A

----> is true

inequality B

---> is true

therefore

The point is a solution of the system of linear inequalities

Case 2) point (2,5)    

For x=2, y=5

inequality A

----> is not true

therefore

The point is not a solution of the system of linear inequalities

Case 3) point (-5,1)    

For x=-5, y=1

inequality A

----> is true

inequality B

---> is not true

therefore

The point is not a solution of the system of linear inequalities

Case 4) point (10,3)    

For x=10, y=3

inequality A

----> is not true

therefore

The point is not a solution of the system of linear inequalities

Case 5) point (2,-10)    

For x=2, y=-10

inequality A

----> is true

inequality B

---> is true

therefore

The point is a solution of the system of linear inequalities

see the attached figure to better understand the problem

If a ordered pair is a solution of the system , then the ordered pair must lie in the shaded area of the solution set

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x

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