Linear Equations in Two Variables

Overview

A concise walkthrough solving two linear equations arising from bottle sales in June and July. Students see how to translate word problems into equations, substitute, and compute the numbers of each bottle type.

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Phases

#	Phase Name	Duration	Description
1	Title	~4s	FadeIn the title "Linear Equations in Two Variables", hold 2 s, then FadeOut.
2	Scene 1 – Problem Statement	~7s	Show the June data ("June", small = ₹10, large = ₹15, total bottles = 1000, total sale = ₹12,750) centered, pause 3 s, then FadeOut.
3	Scene 2 – June Variables Intro	~4s	Show "Let" then $x =$ number of small bottles, $y =$ number of large bottles, pause 2 s, FadeOut.
4	Scene 2 – Bottle Count Equation	~4s	Show "Total bottles = 1000" then equation $x + y = 1000$, pause 2 s, FadeOut.
5	Scene 2 – Sales Equation	~5s	Show "Total sale = ₹12,750" then equation $10x + 15y = 12{,}750$, pause 3 s, FadeOut.
6	Scene 3 – Solve June (Step 1)	~3s	Show $x + y = 1000$, then rewrite as $x = 1000 - y$, pause 1.5 s, FadeOut.
7	Scene 3 – Solve June (Step 2)	~5s	Show $10x + 15y = 12{,}750$, substitute $x = 1000 - y$ to get $10(1000 - y) + 15y = 12{,}750$, pause 2 s, FadeOut.
8	Scene 3 – Solve June (Algebra)	~6s	Sequentially display:

1. $10{,}000 - 10y + 15y = 12{,}750$
2. $5y = 2{,}750$
3. $y = 550$
   each with FadeOut between, total ~4 s, then show $x = 1000 - 550 = 450$, pause 2 s, FadeOut. |
   | 9 | Scene 3 – June Result | ~4s | Show "JUNE" with small bottles = 450, large bottles = 550, pause 3 s, FadeOut. |
   |10| Scene 4 – July Price Change | ~5s | Show "July" and the price increase statement, then display new prices ₹12 and ₹17, pause 3 s, FadeOut. |
   |11| Scene 5 – July Variables Intro | ~4s | Show "Let" then $a =$ small bottles, $b =$ large bottles, pause 2 s, FadeOut. |
   |12| Scene 5 – Bottle Count Equation | ~4s | Show "Total bottles = 2500" then $a + b = 2500$, pause 2 s, FadeOut. |
   |13| Scene 5 – Sales Equation | ~5s | Show "Total sale = ₹34,250" then $12a + 17b = 34{,}250$, pause 3 s, FadeOut. |
   |14| Scene 6 – Solve July (Step 1) | ~3s | Show $a + b = 2500$, then $a = 2500 - b$, pause 1.5 s, FadeOut. |
   |15| Scene 6 – Solve July (Step 2) | ~5s | Show $12a + 17b = 34{,}250$, substitute $a = 2500 - b$ → $12(2500 - b) + 17b = 34{,}250$, pause 2 s, FadeOut. |
   |16| Scene 6 – Solve July (Algebra) | ~6s | Sequentially display:
4. $30{,}000 - 12b + 17b = 34{,}250$
5. $5b = 4{,}250$
6. $b = 850$
   each with FadeOut, then show $a = 2500 - 850 = 1650$, pause 2 s, FadeOut. |
   |17| Scene 7 – Final Answers | ~9s | FadeIn large heading "FINAL ANSWERS", then:

• Show June block (small = 450, large = 550) for 2 s,
• FadeOut, then show July block (small = 1650, large = 850) for 3 s, then FadeOut. |
  |18| Key Idea Summary | ~5s | Show "Key Idea" and the generic forms:
  $$\ ext{Number of bottles} \rightarrow x + y$$
  $$\ ext{Total sale} \rightarrow p_1 x + p_2 y$$
  hold 3 s, then FadeOut. |

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Layout

┌─────────────────────────────────────────────┐
│                                             │
│                MAIN (centered)              │
│   All equations, titles, and labels appear   │
│   here, one at a time, never overlapping.   │
│                                             │
├─────────────────────────────────────────────┤
│  Footer (optional) – small caption or none   │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Main	Title, problem data, each equation, variable names, final answer blocks, key‑idea summary. All centered, large, dark text on light background.	Only one object visible at any moment; previous object fully FadeOut before next appears.
Footer	May hold a brief caption such as "Key Idea" during the last phase; otherwise empty.

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Notes

• Strict rule compliance: No Transform or ReplacementTransform. Every new equation is introduced by a full FadeOut of the previous one, a 0.5 s pause, then a Write (or FadeIn) of the new equation.
• All equations are centered, large, and use dark color for readability; an accent color (e.g., blue) highlights final numeric answers.
• Red is reserved only for optional emphasis (not used here).
• FadeOut duration ≈ 0.5 s; Write duration ≈ 1 s unless the equation is very short.
• Assumptions made:
  1. Standard 16:9 landscape with light gray background.
  2. Uniform pause times as described; minor extra 0.5 s between consecutive equations for the FadeOut/Write cycle.
  3. No additional decorative graphics beyond the textual/math content.
• Total estimated runtime ≈ 58 seconds, comfortably under the 60 s limit.