TI-84 Plus CE: How to Solve Equations

CalcPlex
1 Jan 201904:24
EducationalLearning
32 Likes 10 Comments

TLDRThis tutorial offers a step-by-step guide on solving equations using the TI-84 Plus CE graphing calculator. It begins with solving a basic equation, illustrating the process of inputting the equation into the calculator and using the numeric solver to find the solution. The video then addresses equations with multiple solutions, explaining how the calculator provides the closest solution to the initial input. It highlights limitations, such as the inability to solve equations with multiple variables and the calculator's occasional inaccuracy with infinite solutions or very close approximations. The tutorial concludes with a reminder to be aware of these limitations and a prompt for viewer engagement.

Takeaways
  • 📚 The video is a tutorial on solving equations using the TI 84 Plus CE graphing calculator.
  • 🔍 It covers how to use the equation solver function, accessed by pressing the math button and selecting 'equation solver'.
  • 📝 The tutorial explains how to input equations into the calculator, using two boxes to represent each side of the equation.
  • 🔢 The first example demonstrates solving a basic equation, with steps shown to input '3 + 2x = 4 + 5x' into the calculator.
  • 💡 After inputting the equation, pressing the 'graph' button brings up an initial guess which may not be the correct answer.
  • 🚀 To find the correct solution, the 'solve' button (uf button) is pressed, which provides the accurate result, such as 'X = -1/3'.
  • 🔄 For exiting the equation solver, the video suggests pressing 'second' and then 'mode' to quit.
  • 🔍 The second example addresses solving an equation with multiple solutions, like '0 = x - 3x + 3', where the solutions are x = 3 and x = -3.
  • 🔎 The program provides the solution closest to the initial guess, so typing in different numbers and solving can help find all solutions.
  • 🚫 The video points out limitations, such as the inability to solve equations with multiple variables or infinite solutions.
  • ⚠️ It also warns about potential inaccuracies, where the calculator might give a very close but not exact answer, like '2.999...' instead of '3'.
Q & A

  • What is the purpose of the video tutorial?

    -The purpose of the video tutorial is to teach viewers how to solve equations on the TI 84 plus CE graphing calculator.

  • How do you access the equation solver on the TI 84 plus CE calculator?

    -To access the equation solver, press the math button followed by the last option in the menus, or quickly by pressing the up arrow key and then pressing enter to select the numeric solver.

  • What does the 'e^2' button represent on the calculator?

    -The 'e^2' button on the calculator represents the right side of the equation when solving equations.

  • How do you input an equation into the calculator?

    -You input an equation by typing the left side of the equation first, then pressing the down arrow key to get to 'e^2' which is the right side of the equation, and typing that in as well.

  • What does the calculator initially display after pressing the 'ok' button?

    -After pressing the 'ok' button, the calculator initially displays 'x equals 0 or x equals some random number', which is not necessarily the correct answer but the answer to the previous equation or the stored value in X.

  • What button do you press to get the correct answer after typing in the equation?

    -To get the correct answer, press the solve button, which is the 'uf' button on the calculator.

  • Why might the calculator give an incorrect solution for an equation with multiple solutions?

    -The calculator might give an incorrect solution because it provides the answer closest to whatever value is typed in the X register, not necessarily all the solutions.

  • What is the limitation of the calculator when dealing with equations with multiple unknown variables?

    -The calculator cannot solve equations with multiple unknown variables; it assumes the other variables are equal to zero and only solves for the variable you are inputting.

  • What issue arises when solving equations with infinite solutions on the calculator?

    -The calculator might not indicate that there are infinite solutions and will just say that whatever number is typed in is the correct answer.

  • How can the calculator sometimes give an incorrect solution for a simple equation?

    -The calculator might give an incorrect solution, such as '2.999...' instead of '3', due to rounding or precision limitations.

  • What is the recommended action if you have an equation with multiple solutions and want to find all of them?

    -The recommended action is to keep typing in random numbers and hitting solve until you find all the solutions, as there isn't a better way to do that with the calculator.

Outlines
00:00
📚 Introduction to Solving Equations on TI 84 Plus CE

This paragraph introduces a tutorial on solving equations using the TI 84 Plus CE graphing calculator. The speaker outlines the plan to demonstrate solving basic equations, equations with multiple solutions, and discusses the limitations of the calculator's equation solver. The process begins with accessing the equation solver via the math menu and involves entering the equation's two sides into the calculator. The example given is a simple linear equation, 3 + 2x = 4 + 5x, which the speaker solves step by step, explaining how to input the equation and use the 'solve' function to find the value of x.

🔍 Solving Equations with Multiple Solutions

The speaker proceeds to solve an equation with multiple solutions, specifically 0 = x - 3x + 3, which has solutions x = 3 and x = -3. The process involves re-entering the equation into the equation solver and using the 'solve' function. The calculator initially provides an incorrect solution, but by typing in a number close to one of the correct solutions, the speaker demonstrates how the calculator can be coaxed into providing the correct answer. The paragraph highlights the trial-and-error nature of finding all solutions when dealing with multiple solutions on the TI 84 Plus CE.

🚫 Limitations of the Equation Solver on TI 84 Plus CE

The tutorial concludes by addressing the limitations of the TI 84 Plus CE's equation solver. The speaker explains that the calculator cannot solve equations with multiple variables, as it assumes other variables are zero unless specified. Additionally, the solver may not recognize equations with infinite solutions, instead reflecting the input value as the 'correct' answer. The speaker also notes that the calculator can sometimes provide an approximate value, such as 2.999..., instead of the exact solution, such as 3. The paragraph serves as a cautionary note for users to be aware of these limitations when using the equation solver.

Mindmap
Keywords
💡TI 84 Plus CE
The TI 84 Plus CE is a graphing calculator made by Texas Instruments, known for its advanced capabilities in solving mathematical problems. In the video's context, it is the primary tool used to demonstrate how to solve equations. The script mentions it as the device on which the equation solver feature is used, indicating its relevance to the tutorial's theme.
💡Equation Solver
The Equation Solver is a function within the TI 84 Plus CE calculator that allows users to solve equations. The script explains how to access this feature by pressing the 'math' button and selecting the 'equation solver' option. It is central to the video's educational purpose, as it guides viewers through the process of solving equations using this tool.
💡Basic Equation
A basic equation in mathematics is a simple statement that expresses the equality of two mathematical expressions, often involving variables. In the script, the presenter begins by showing how to solve a basic equation on the TI 84 Plus CE, such as '3 + 2x = 4 + 5x', to introduce the concept of using the calculator for equation solving.
💡Multiple Solutions
An equation with multiple solutions has more than one value for the variable that satisfies the equation. The script discusses an example equation, '0 = x - 3x + 3', which has solutions x = 3 and x = -3. The presenter explains how the calculator's equation solver can find one solution but may require multiple attempts to find all solutions.
💡Limitations
Limitations refer to the constraints or restrictions of a tool or method. The video script mentions the limitations of the TI 84 Plus CE's equation solver, such as its inability to solve equations with multiple variables or to accurately indicate infinite solutions. These limitations are important for users to understand to set realistic expectations when using the calculator.
💡Numeric Solver
The numeric solver is a specific mode within the equation solver function on the TI 84 Plus CE that deals with numerical solutions. The script instructs viewers to press the up arrow key and then enter to select the numeric solver, which is used to solve for numerical values of variables in equations.
💡Graph Button
The graph button on the TI 84 Plus CE calculator is used to initiate certain functions, including the equation solver. In the script, pressing the graph button is mentioned as the step to proceed after inputting an equation into the solver, indicating its role in navigating the calculator's interface.
💡Solve Button
The solve button, represented by the 'uf' button in the script, is used to execute the solving process in the equation solver on the TI 84 Plus CE. It is a crucial step in the solving process, as pressing this button will provide the calculator's solution to the input equation.
💡Multiple Variables
An equation with multiple variables involves more than one unknown quantity that needs to be solved for. The script points out that the TI 84 Plus CE's equation solver has limitations when it comes to equations with multiple variables, such as 'x + y = 3', as it can only solve for one variable at a time, assuming the others are zero.
💡Infinite Solutions
An equation with infinite solutions is one where any value of the variable satisfies the equation. The script provides the example 'x - x = 0', which has infinite solutions, and notes that the calculator will not explicitly state this but will instead validate any number entered as correct.
💡Approximation
Approximation refers to a value that is close to the exact value but not exact. In the context of the script, when the calculator provides a solution like '2.999...' for an equation where the exact solution is '3', it is an approximation. The video emphasizes the importance of recognizing such approximations as equivalent to the exact solution.
Highlights

Introduction to a quick tutorial on solving equations using the TI 84 plus CE graphing calculator.

Explanation of how to access the equation solver feature on the calculator.

Demonstration of solving a basic equation by entering the equation into the calculator.

Clarification on how to input variables and equations into the calculator using the 'X T theta n' button.

Instructions on using the 'graph' button to initiate the equation solving process.

Note on the initial solution provided by the calculator not necessarily being the correct answer.

Use of the 'solve' button to find the accurate solution for the equation.

Exiting the equation solver by using 'second' and 'mode' which corresponds to 'quit'.

Approach to solving equations with multiple solutions using the calculator.

Example of solving an equation where the solutions are x equals 3 and x equals -3.

Description of the calculator's behavior when providing the closest solution to the inputted number.

Strategy for finding all solutions to an equation with multiple solutions by inputting random numbers.

Limitations of the calculator when dealing with equations involving multiple variables.

Behavior of the calculator when presented with an equation that has infinite solutions.

Potential issue of the calculator providing an approximate solution instead of the exact one.

Advice on recognizing when the calculator's solution is an approximation of the exact value.

Closing remarks encouraging viewers to like the video and look forward to the next one.

Transcripts

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