# Write a system of inequalities that has no solution symbol Determine Whether an Ordered Pair is a Solution to a System of Linear Inequalities On the graph above, you can see that the points B and N are solutions for the system because their coordinates will make both inequalities true statements.

Determine whether the ordered pair is a solution to the system. Let me graph a couple more points here just so that I make sure that I'm drawing it reasonably accurately. Define Solutions to Systems of Linear Inequalities Learning Outcomes Identify solutions to systems of linear inequalities Graph a System of Two Inequalities Remember from the module on graphing that the graph of a single linear inequality splits the coordinate plane into two regions.

### Write a system of inequalities for the shaded region

Both inequalities define larger individual bounded regions, but the range of possible solutions for the system will consist of the smaller bounded region that they have in common. There's the empty set. In contrast, points M and A both lie outside the solution region purple. System of Linear Inequalities Two or more linear inequalities grouped together form a system of linear inequalities. A good place to start is just to graph the solution sets for each of these inequalities and then see where they overlap. The general steps are outlined below: Graph each inequality as a line and determine whether it will be solid or dashed. The second inequality is y is less than 2x minus 5. The colored area, the area on the plane that contains all possible solutions to an inequality, is called the bounded region. On the graph, you can see that the points B and N provide possible solutions for the system because their coordinates will make both inequalities true statements. When the graphs of a system of two linear equations are parallel to each other, we found that there was no solution to the system.

Luckily, graphs can provide a shortcut. This area up here satisfies the last one and the first one. The points M and N are plotted within the bounded region. We will verify algebraically whether a point is a solution to a linear equation or inequality. To determine if an ordered pair is a solution to a system of two inequalities, we substitute the values of the variables into each inequality.

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