Precalculus (6th Edition) Blitzer

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 $5x-y\le 10$.