Which point lies in the solution set for the following system of inequalities?

Question

y > x + 4 y > -x + 2

(1, 6)

(-2, -1)

(-3, 2)

(1, 1)

Answer 1

Given system of inequalities are y > x+4 and  y > -x+2

Given points are (1 , 6) , (-2 , -1) , (-3 , 2) , (1 , 1)

Substitute (1 , 6) in the given system of inequalities

Here x = 1 and y = 6

6 > 1+4 and 6 > -1+2

6 > 5 and 6 > 1 (it is true)

Substitute (-2 , -1) in the given system of inequalities

Here x = -2 and y = -1

-1 > -2+4  and -1 > -(-2)+2

-1 > 2 and -1 > 4 (it is false)

Substitute (-3 , 2) in the system of inequalities

Here x = -3 and y = 2

2 > -3+4 and 2 > -(-3)+2

2 > 1 and 2 > 5 (it is false)

Substitute (1 , 1) in the system of inequalities

Here x = 1 and y = 1

1 > 1+4 and 1 > 1+2

1 > 5 and 1 > 3 (it is false)

Therefore the points (1 , 6) is satisfying the system of equalities