Question

Prove if the test point (2,-3) is a solution to the system:3x+y≥ -3x+2y ≤ 4

Answer 1

To solve this question, we can substitute the given point into the inequalities. That is, by substituying x=2 and y=-3 into the first inequality, we obtain

`3(2)+(-3)\ge-3`

and the left hand side is equal to 6-3=3. Because 3>-3, the point (2,-3) can be a solution. However, we must be the same for the remaining inequality, that is, by substituying x=2 and y=-3 into the second inequality, we have

`2+2(-3)\leq4`

and the left hand side is equal to 2-6=-4, then -4<4.

With both results, we can conclude that the point (2,-3) is a solution of the system.