Solving Equations with 2 Variables

🎬 Video Tutorial

  • (0:01) Equations with Two Variables: In equation $x + 2y = 20$, $x$ represents cookies, $y$ represents sandwiches, and £20 budget.
  • (1:00) Substituting Values: By plugging in $x = 10$ to find $y = 5$, meaning you can afford 10 cookies and 5 sandwiches. Similarly, substitute $y = 8$ to get $x = 4$.
  • (1:53) Graphing linear equations: Rewrite the equation in terms of $y$, giving $y = 10 – 0.5x$, and plot this to see the relationship between $x$ and $y$ visually.
  • (2:36) Solution combinations: Each point on the line represents a possible combination of cookies and sandwiches (e.g., $(8, 6)$ means $x=8, y=6$).

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Solving Equations with 2 Variables

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Q: You have $20. Each snack costs $2, and each water costs $1. Use $x$ for the number of snacks and $y$ for the number of waters. How would you form the equation?

 

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Q: You have $30. Each apple costs $3, and each orange costs $2. Use $x$ for the number of apples and $y$ for the number of oranges. How would you form the equation?

 

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Q: You have $40. Each pencil costs $2, and each eraser costs $3. If you buy 5 pencils, how many erasers can you still afford?

 

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Q: You have $40. Each pencil costs $2, and each eraser costs $3. If you buy 8 erasers, how many pencils can you still afford?

 

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Q: You have $40. Each pencil costs $2, and each eraser costs $3. If you buy 6 pencils and 3 erasers, how much money will you have left?

 

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Q: You have $40. Each pencil costs $2, and each eraser costs $3. In the graph below, what does point P mean?

The equation represented is 2x + 3y = 40, where x is the number of pencils and y is the number of erasers. Point P shows x = 5 and y = 10, meaning 5 pencils and 10 erasers can be purchased.

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