Algebra 41 - Using Systems of Equations Versus One Equation

TL;DR

Linear equations can be used to solve various types of problems including finding dimensions, solving motion problems, and calculating prices.

Transcript

Hello. I'm Professor Von Schmohawk and welcome to Why U. So far we have discussed methods of solving systems of two linear equations in two variables including the substitution method and the elimination method. We also showed how a system of linear equations could be used to find the time and place where two runners starting at different times in ... Read More

Key Insights

• 🅰️ Systems of linear equations can be used to solve various types of problems, including finding dimensions, solving motion problems, and calculating prices.
• 🔂 Some problems can be solved using a single equation with one variable, while others may require a system of equations with multiple variables.
• 😄 The method chosen to solve a problem depends on its complexity and the ease of elimination or substitution.

Questions & Answers

Q: How did we solve the problem of finding the dimensions of three identical dog pens without creating systems of equations?

We created a single equation with one variable (width) and expressed both the length and width of a pen in terms of that variable. We then solved that equation to find the width.

Q: Can the problem of determining the speeds of a car and a bus be solved using a single equation with one variable?

Yes, by expressing one unknown (speed of the car or bus) in terms of the other, we can substitute that expression into the equation to eliminate one variable. However, this is equivalent to solving a system of equations using the substitution method.

Q: How did we solve the problem of calculating the pricing at a theater for tickets and drinks using a system of equations?

We created a system of two equations, one for the total cost of tickets and drinks for each group, and used the elimination method to eliminate one variable and solve for the other. This allowed us to find the prices of tickets and drinks.

Summary & Key Takeaways

• Linear equations can be used to find the dimensions of three identical dog pens, where each pen's length must be twice its width plus 3 feet.

• Linear equations can also be used to solve motion problems, such as determining the speeds of a car and a bus traveling in opposite directions on a highway.

• Linear equations can be used to calculate the pricing at a theater for tickets and drinks, given the total cost of tickets and drinks for two different groups.