# Write a system of linear inequalities that has no solution inequalities

So this graph is going to look something like this. 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.

System of Linear Inequalities Two or more linear inequalities grouped together form a system of linear inequalities.

The following example shows how to test a point to see whether it is a solution to a system of inequalities. If we move forward 2, we'll move up 4, just like that. So before we even get to this last inequality, in order for there to be something that satisfies both of these inequalities, it has to be in both of their solution sets. The line is dashed as points on the line are not true.

We will verify algebraically whether a point is a solution to a linear equation or inequality. Note how they have the same slopes.

Graphing two-variable linear inequalities Video transcript We're asked to determine the solution set of this system, and we actually have three inequalities right here.

Introduction In a system of equations, the possible solutions must be true for all of the equations. On one side lie all the possible solutions to the inequality. To solve a system of linear inequalities, we will find values of the variables that are solutions to both inequalities. On the other side, there are no solutions. That's the graph of y is equal to 2x plus 1.

## Write a system of linear inequalities to define the profit regions.

So 2x minus 5, the y-intercept is negative 5. So, the shaded area shows all of the solutions for this inequality. 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. If x is 0, y is 1, and the slope is 2. They're separated by this kind of no-man's land between these two parallel lines. All possible solutions must be true for all of the inequalities. Show Solution Check the point with each of the inequalities. See the purple area, where the bounded regions of the two inequalities overlap?
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