Linear Equation Solutions
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Linear Equation Solutions
📊 Part 1: Identifying Solution Types
a) 3x + 5 = 2x + 8
This equation has:
One solution No solution Infinitely many solutionsb) 4x - 7 = 4x + 2
This equation has:
One solution No solution Infinitely many solutionsc) 2(x + 3) = 2x + 6
This equation has:
One solution No solution Infinitely many solutions🌍 Part 2: Real-World Applications
Company A: Cost = $3 per mile + $2 base fee
Company B: Cost = $3 per mile + $5 base fee
a) Write equations for both companies (use C for cost and m for miles):
Company A: C = _______________
Company B: C = _______________
b) Set the equations equal to find when costs are the same:
c) What does your answer tell you about when these taxi companies cost the same?
Plan X: $25 per month + $0.10 per text
Plan Y: $25 per month + $0.10 per text
If you set up an equation to find when these plans cost the same, what type of solution would you expect and why?
🔍 Part 3: Analysis and Explanation
a) Two parallel lines: _______________
b) Two intersecting lines: _______________
c) Two identical overlapping lines: _______________
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