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 , and the region below this line is shaded.
- The green line represents , 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:
- How do you solve a system of linear inequalities algebraically?
- What is the significance of using solid or dashed lines when graphing inequalities?
- How do you find the intersection points of two lines algebraically?
- Can a system of linear inequalities have no solution? Why?
- 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
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