Linear Equations: Substitution and Elimination Methods
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Questions and Answers

What is the first step in the substitution method for solving systems of linear equations?

  • Substitute the expression from one equation into the other equation
  • Add or subtract the equations to eliminate a variable
  • Choose one of the equations and solve for one variable (correct)
  • Multiply both equations by necessary multiples

    • In the substitution method, what is the purpose of step 2?

  • To substitute the expression from one equation into the other equation (correct)
  • To solve for the other variable
  • To eliminate one variable
  • To simplify the equations

    • What is the main advantage of the elimination method?

  • It is easy to visualize the solution
  • It is always the most efficient method
  • It is a graphical method
  • It is often used when the coefficients of one variable are easily made equal (correct)

    • What is the final step in both the substitution and elimination methods?

    <p>Substitute the value of the variable back into one of the original equations</p> Signup and view all the answers

    When is the substitution method often used?

    <p>When one equation is easily solvable for one variable</p> Signup and view all the answers

    What is the purpose of step 3 in the elimination method?

    <p>To simplify and solve for the remaining variable</p> Signup and view all the answers

    Which method is often used when the coefficients of one variable are easily made equal?

    <p>Elimination method</p> Signup and view all the answers

    What is the main difference between the substitution and elimination methods?

    <p>The substitution method involves substituting one equation into another, while the elimination method involves eliminating one variable</p> Signup and view all the answers

    What is the term for organisms that produce their own food?

    <p>Autotrophic</p> Signup and view all the answers

    What is the overall equation for photosynthesis?

    <p>6 CO2 + 6 H2O + light energy → C6H12O6 + 6 O2</p> Signup and view all the answers

    Where do light-dependent reactions occur in photosynthesis?

    <p>Thylakoid membranes</p> Signup and view all the answers

    What is the term for the process of generating energy from glucose?

    <p>Respiration</p> Signup and view all the answers

    What is the byproduct of anaerobic respiration in muscle cells?

    <p>Lactic acid</p> Signup and view all the answers

    What is the first stage of aerobic respiration?

    <p>Glycolysis</p> Signup and view all the answers

    What is the term for organisms that cannot produce their own food?

    <p>Heterotrophic</p> Signup and view all the answers

    What is the term for the process of absorbing nutrients from dead organic matter?

    <p>Saprotrophic</p> Signup and view all the answers

    What is the term for the process of obtaining nutrients from another living organism?

    <p>Parasitic</p> Signup and view all the answers

    Study Notes

    Linear Equations

    Substitution Method

    • A method used to solve systems of linear equations by substituting one equation into another
    • Steps:
      1. Choose one of the equations and solve for one variable (e.g. x or y)
      2. Substitute the expression from step 1 into the other equation
      3. Simplify and solve for the other variable
      4. Substitute the value of the variable back into one of the original equations to find the value of the other variable

    Elimination Method

    • A method used to solve systems of linear equations by eliminating one variable
    • Steps:
      1. Multiply both equations by necessary multiples such that the coefficients of one variable (e.g. x or y) are the same
      2. Add or subtract the equations to eliminate the variable
      3. Simplify and solve for the remaining variable
      4. Substitute the value of the variable back into one of the original equations to find the value of the other variable

    Key Points

    • Both methods can be used to solve systems of linear equations
    • The substitution method is often used when one equation is easily solvable for one variable
    • The elimination method is often used when the coefficients of one variable are easily made equal
    • Graphing can also be used to solve systems of linear equations, but is not always the most efficient method

    Linear Equations Solutions

    Substitution Method

    • Solves systems of linear equations by substituting one equation into another
    • Steps involve choosing an equation, solving for one variable, substituting into the other equation, simplifying, and solving for the other variable
    • Involves back-substitution to find the value of the other variable

    Elimination Method

    • Solves systems of linear equations by eliminating one variable
    • Steps involve multiplying equations to make coefficients equal, adding or subtracting to eliminate a variable, simplifying, and solving for the remaining variable
    • Involves back-substitution to find the value of the other variable

    Key Points

    • Both substitution and elimination methods can be used to solve systems of linear equations
    • Substitution method is suitable when one equation is easily solvable for one variable
    • Elimination method is suitable when coefficients of one variable can be easily made equal
    • Graphing can also be used to solve systems of linear equations, but may not always be the most efficient method

    Nutrition

    • Autotrophic nutrition: organisms produce their own food, e.g., plants
    • Heterotrophic nutrition: organisms cannot produce their own food, e.g., animals

    Modes of Nutrition

    • Holozoic nutrition: ingestion of solid food particles, e.g., animals
    • Saprotrophic nutrition: absorption of nutrients from dead organic matter, e.g., fungi
    • Parasitic nutrition: obtaining nutrients from another living organism, e.g., parasites

    Photosynthesis

    • Definition: process by which plants, algae, and some bacteria convert light energy into chemical energy
    • Overall equation: 6 CO2 + 6 H2O + light energy → C6H12O6 (glucose) + 6 O2
    • Light-dependent reactions: occur in thylakoid membranes, light energy excites electrons to generate ATP and NADPH
    • Light-independent reactions (Calvin Cycle): occur in stroma, ATP and NADPH are used to convert CO2 into glucose

    Respiration

    • Definition: process by which cells generate energy from glucose
    • Types of respiration:
      • Aerobic respiration: occurs in presence of oxygen, produces ATP and water
      • Anaerobic respiration: occurs in absence of oxygen, produces ATP and lactic acid or ethanol

    Stages of Aerobic Respiration

    • Glycolysis: breakdown of glucose into pyruvate
    • Citric Acid Cycle (Krebs Cycle): breakdown of pyruvate into ATP, NADH, and FADH2
    • Electron Transport Chain: generation of ATP from NADH and FADH2
    • Oxidative Phosphorylation: production of ATP from energy released during electron transport

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    Description

    Learn about the substitution and elimination methods to solve systems of linear equations. Understand the steps involved in each method and practice solving problems.

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