Page 752 - Algebra 1

Remember that a system of equations is inconsistent when there are no solutions. This occurs when the slopes of the lines are the same and the y-intercepts are different.
The system has no solutions because the lines are parallel.
y = - _2 x - 2 3
y = - _2 x + 3 3
When the equal signs in these equations are replaced with inequality symbols, the system may or may not have a solution set.
Solving Systems of Inequalities with Parallel Boundary Lines
Graph each system.
a. y ≤ -_2 x - 2 3
y ≥ - _2 x + 3 3
SOLUTION
The two solution sets do not intersect, so the system has no solution.
b . y ≥ - _2 x - 2 3
y ≤ - _2 x + 3 3
SOLUTION
The solution set is the region between the parallel lines.
c. y ≥ -_2 x - 2 3
y ≥ - _2 x + 3 3
SOLUTION
Thesolutionsof y≥-_2x+3areasubsetof 3
the solutions of y ≥ -_2x - 2. 3
The solutions of the system are the same as the solutions of y ≥ -_2 x + 3. 3
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Example
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Math Reasoning
Generalize When the boundary lines are parallel, what must be true about the inequality symbols for one graph to be a subset of the other?
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Lesson 109 737