Answer
To determine if an ordered pair can be a solution of an inequality of two variables, put the values of x and y equal to the values in the ordered pair.
Work Step by Step
Solutions to an equation are the values of x and y, which when put into the equation, satisfy it.
So, to determine whether an ordered pair is a solution of the inequality of two variables, put the values of x and y equal to the values of the ordered pair and check if the values satisfy the inequality.
Example:
Assume a linear inequality, $5x-y\le 10$ and consider the ordered pairs $\,\,\left( 3,-4 \right),\,\left( -1,2 \right)$; to check whether they are solutions of the inequality or not:
Put the value of the first ordered pair $\,\left( 3,-4 \right)$ in the equation $5x-y\le 10$ as shown below:
$\begin{align}
& 5\left( 3 \right)-\left( -4 \right)\le 10 \\
& 15+4\le 10 \\
& 19\le 10 \\
\end{align}$
Thus, the ordered pair does not satisfy the inequality.
Put the value of the second ordered pair $\left( -1,2 \right)$ in the equation $5x-y\le 10$,
$\begin{align}
& 5\left( -1 \right)-\left( 2 \right)\le 10 \\
& -5-2\le 10 \\
& -7\le 10 \\
\end{align}$
Thus, the second ordered pair is correct.
Thus, $\left( -1,2 \right)$ is a solution of the linear inequality $5x-y\le 10$.
