Question

b. are (-1,1) and (4,1) solutions to the inequality 2y - 3x < 5? explain how you know.

Explanation:

Step1: Substitute (-1,1) into the inequality

Substitute \(x=-1\) and \(y = 1\) into \(2y-3x<5\). We get \(2\times1-3\times(-1)\).
\[2\times1 - 3\times(-1)=2 + 3=5\]
Since \(5
less5\) (it is equal), \((-1,1)\) is not a solution.

Step2: Substitute (4,1) into the inequality

Substitute \(x = 4\) and \(y=1\) into \(2y-3x<5\). We get \(2\times1-3\times4\).
\[2\times1-3\times4=2 - 12=-10\]
Since \(-10<5\), \((4,1)\) is a solution.

Answer:

The point \((4,1)\) is a solution to the inequality \(2y - 3x<5\) and the point \((-1,1)\) is not a solution.