Math Problem Statement

Graph the solution of the system of linear inequalities. StartSet Start 2 By 1 Matrix 1st Row 1st Column 5 x minus 4 y less than or equals 20 2nd Row 1st Column y less than or equals minus 5 EndMatrix

Solution

Here is the graph of the system of linear inequalities:

  • The blue line represents 5x4y=205x - 4y = 20, and the region below this line is shaded.
  • The green line represents y=5y = -5, and the region below this horizontal line is also shaded.
  • The overlapping shaded region is the solution to the system of inequalities.

Would you like more details or have any specific questions?

Here are 5 related questions for further exploration:

  1. How do you solve a system of linear inequalities algebraically?
  2. What is the significance of using solid or dashed lines when graphing inequalities?
  3. How do you find the intersection points of two lines algebraically?
  4. Can a system of linear inequalities have no solution? Why?
  5. How do you check if a point lies within the solution region of a system of inequalities?

Tip: Always test a point (like the origin) to verify which side of the boundary lines to shade!

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Math Problem Analysis

Mathematical Concepts

Linear Inequalities
Systems of Inequalities
Coordinate Geometry

Formulas

Linear equation form: ax + by = c
Slope-intercept form: y = mx + b

Theorems

Inequality Theorem
Slope Theorem

Suitable Grade Level

Grades 8-10