Determine if the test point is a solution to the system of l

Determine if the test point is a solution to the system of linear inequalities. (3, 1) x - y 3 (0, 0) x - 2y -1 (-2, 3) 3x - 2y 1 -x + 3y > 3 (1, 2) 2x - 2y -1 (4, -2) x - 2y 8 -2x - 5y > 0 (-1, -2) x + y

Solution

I will solve 45 to 47questions

45). (3,1)

inequalities are x-y <3

x+y >3

plug point in the 1st inequality 3 -1 <3

2 < 3 false ,

if we plug point in 2nd inequality then we get 4 >3 true

to be a solution the point has to satisfy both equations

so we can say this point is not a solution

46). (0,0)   

x-2y <1 2x -y >-1

0 -0<1 2(0) -0 >-1

0 <1 (true) 0 >-1 (true)

so both inequalities are true

the point is a solution

47).(-2,3)

3x -2y >=1 -x+2y >3

3(-2) -2(3) >= 1 -(-2) +2(3) >3

-6 -6 >=1 2 +6 >3

-12 >= 1 (false) 8> 3 (true)

the point is not solution