It certainly looks like a mistake. If the diagram is meant to illustrate the inequalities then the third inequality should be $5x+8y\le40$.swag312 said:
A system of linear inequalities is a set of two or more linear inequalities with the same variables. These inequalities are connected by logical operators such as "and" or "or" and represent the constraints or boundaries of a problem.
To solve a system of linear inequalities, you can use a graphing method or an algebraic method. In the graphing method, you plot each inequality on a coordinate plane and find the overlapping region. In the algebraic method, you manipulate the inequalities to isolate the variables and find the solution set.
A possible mistake in a system of linear inequalities could be an incorrect sign or operation when manipulating the inequalities. For example, changing a "less than" sign to a "greater than" sign can completely change the solution set.
To check for mistakes in a system of linear inequalities, you can plug in the solution set into each inequality and see if it satisfies the inequality. If it does not, then there may be a mistake in the system.
Yes, a system of linear inequalities can have no solution if the inequalities are contradictory or if the solution set is empty. This means that there is no point that satisfies all of the inequalities in the system.