Question

The inequality 2x - 3y ≥ 5 is satisfied by point (1/2,1/3 ). True False

Answer 1

False

Explanation:

(1/2, 1/3) ⇒ x = 1/2 and y = 1/3

Substitute these values in the given equation;

2x - 3y ≥ 5

2(1/2) - 3(1/3) ≥ 5

`(2)/(2)` -
`(3)/(3)`

= 1 - 1 = 0

Thus the inequality is not satisfied by the given points, since 0 < 5 and ≠ 5.

Answer 2

For this case we evaluate the following inequality in the given point and verify if it is met:

`2x-3y\geq  5`

`(x, y) = (\frac {1} {2}, \frac {1} {3})`

Substituting:

`2 \frac {1} {2} -3 \frac {1} {3}\geq5`

`1-1\geq 5\\0\geq 5`

It is not fulfilled!

The point does not satisfy the inequality

ANswer:

False