# Which graph shows the solution to the system of linear inequalities: y < 2x - 5, y > -3x + 1?

Updated on January 19, 2024

Answer: To identify the correct graph, look for the region where the shading of y < 2x - 5 and y > -3x + 1 overlap.

## Graphing Linear Inequalities

A system of linear inequalities represents a set of constraints. The solution is the region where the solutions to individual inequalities overlap. For the system y < 2x - 5 and y > -3x + 1, you would graph both inequalities and identify the overlapping region. This concept is crucial in linear programming and optimization, where it’s used to find the best solution under given constraints.

## FAQ on Graphing Linear Inequalities

### How do you graph a linear inequality?

Graph the corresponding equation, then shade above or below the line based on the inequality.

### What does the shading represent on a graph of an inequality?

The shading represents all the solutions to the inequality.

### How do you find the solution to a system of inequalities?

Graph each inequality and then identify the region where the solutions overlap.