Question

The point (-2, -1) satisfies which of the following inequalities? 5x - 2y + 1 > 0
-5x + 2y + 1 > 0
-2x + 5y - 1 > 0
2x + 5y - 1 > 0

Answer 1

We can plug the given point in each equation and check if it satisfies it

1.

5x - 2y + 1 > 0

5(-2)-2(-1)+1>0

-10+2+1>0

-7>0 (false)

2.

-5x + 2y + 1 > 0

-5(-2) + 2(-1) + 1 > 0

10-2+1>0

9>0

so -5x + 2y + 1 > 0 satisfies the given point (-2,-1)

Answer 2

we are given point (-2, -1)

we can plug this point into inequality and check whether it holds true

(a)

$5x - 2y + 1 > 0$

now, we can plug x=-2 and y=-1

$5*-2 - 2*-1 + 1 > 0$

$-10 +2 + 1 > 0$

$-7 > 0$

this is not possible

point (-2,-1) does not satisfy inequality

(B)

$-5x +2y + 1 > 0$

now, we can plug x=-2 and y=-1

$-5*-2 +2*-1 + 1 > 0$

$10 -2 + 1 > 0$

$9 > 0$

this is true

point (-2,-1) does satisfy inequality

(C)

$-2x +5y - 1 > 0$

now, we can plug x=-2 and y=-1

$-2*-2 +5*-1 - 1 > 0$

$4 -5 - 1 > 0$

$-2 > 0$

this is not true

point (-2,-1) does not satisfy inequality

(D)

$2x +5y - 1 > 0$

now, we can plug x=-2 and y=-1

$2*-2 +5*-1 - 1 > 0$

$-4 -5 - 1 > 0$

$-10 > 0$

this is not true

point (-2,-1) does not satisfy inequality

so,

option-B.........Answer