Question

b. check if each of these points is a solution to the inequality 2y - x > 1: (-7,-3) (-6,3) (8,\frac{1}{2}) (0,2)

Explanation:

Step1: Substitute point (-7, - 3)

Substitute \(x=-7\) and \(y = - 3\) into \(x-2y>1\). We get \(-7-2\times(-3)\).
\[

$$\begin{align*} -7-2\times(-3)&=-7 + 6\\ &=-1 \end{align*}$$

\]
Since \(-1<1\), (-7, - 3) is not a solution.

Step2: Substitute point (-6,3)

Substitute \(x = - 6\) and \(y=3\) into \(x - 2y>1\). We get \(-6-2\times3=-6 - 6=-12\). Since \(-12<1\), (-6,3) is not a solution.

Step3: Substitute point \((8,\frac{1}{2})\)

Substitute \(x = 8\) and \(y=\frac{1}{2}\) into \(x-2y>1\). We get \(8-2\times\frac{1}{2}=8 - 1 = 7\). Since \(7>1\), \((8,\frac{1}{2})\) is a solution.

Step4: Substitute point (0,2)

Substitute \(x = 0\) and \(y = 2\) into \(x-2y>1\). We get \(0-2\times2=-4\). Since \(-4<1\), (0,2) is not a solution.

Answer:

The point \((8,\frac{1}{2})\) is a solution to the inequality \(x - 2y>1\), while the points (-7,-3), (-6,3) and (0,2) are not.