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