Solving Systems of Linear Equations
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Questions and Answers

What is a system of linear equations?

  • A set of two or more linear equations that have the same slope.
  • A set of two or more linear equations that have no solution.
  • A set of two or more linear equations that must be true at the same time. (correct)
  • A set of two or more linear equations that have the same solution.

    • Which of the following methods is used to solve systems of linear equations?

  • Elimination method only
  • Substitution method only
  • Graphical method only
  • All of the above (correct)

    • What is the slope-intercept form of a linear equation?

  • y = mx + b (correct)
  • y = mx / b
  • y = mx * b
  • y = mx - b

    • What is the purpose of the slope-intercept form of a linear equation?

    <p>To graph linear equations and identify the slope and y-intercept</p> Signup and view all the answers

    What is the standard form of a linear equation?

    <p>Ax + By = C</p> Signup and view all the answers

    What is the purpose of the standard form of a linear equation?

    <p>To write linear equations in a consistent format and solve systems of linear equations</p> Signup and view all the answers

    How can the standard form of a linear equation be converted to slope-intercept form?

    <p>By rearranging the equation to isolate y and dividing by the coefficient of y (if necessary)</p> Signup and view all the answers

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

    <p>Solve one equation for one variable</p> Signup and view all the answers

    What is the final step in the elimination method for solving systems of linear equations?

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

    Study Notes

    Solving Systems Of Equations

    • A system of linear equations is a set of two or more linear equations that must be true at the same time.
    • Systems of equations can be solved using:
      • Substitution method
        • Elimination method
      • Graphical method

    Substitution Method

    • Solve one equation for one variable
    • Substitute the expression into the other equation
    • Solve for the other variable
    • Substitute the value of the variable back into one of the original equations to find the value of the other variable

    Elimination Method

    • Make the coefficients of one variable opposites
    • Add the equations to eliminate the variable
    • Solve for the remaining variable
    • Substitute the value of the variable back into one of the original equations to find the value of the other variable

    Slope-Intercept Form

    • The slope-intercept form of a linear equation is given by:
      • y = mx + b
      • m is the slope (rate of change)
      • b is the y-intercept (point where the line crosses the y-axis)
    • Slope-intercept form is useful for:
      • Graphing linear equations
      • Identifying the slope and y-intercept of a line

    Standard Form

    • The standard form of a linear equation is given by:
      • Ax + By = C
      • A, B, and C are integers
      • A and B are not both zero
    • Standard form is useful for:
      • Writing linear equations in a consistent format
      • Solving systems of linear equations
    • Standard form can be converted to slope-intercept form by:
      • Rearranging the equation to isolate y
      • Dividing by the coefficient of y (if necessary)

    Systems of Linear Equations

    • A system consists of two or more linear equations that must be true at the same time
    • Can be solved using three methods: Substitution, Elimination, and Graphical method

    Solving Systems of Equations using Substitution Method

    • Solve one equation for one variable
    • Substitute the expression into the other equation to solve for the other variable
    • Substitute the value of the variable back into one of the original equations to find the value of the other variable

    Solving Systems of Equations using Elimination Method

    • Make the coefficients of one variable opposites
    • Add the equations to eliminate the variable
    • Solve for the remaining variable
    • Substitute the value of the variable back into one of the original equations to find the value of the other variable

    Slope-Intercept Form

    • Equation is given by: y = mx + b
    • m represents the slope (rate of change)
    • b represents the y-intercept (point where the line crosses the y-axis)
    • Useful for graphing linear equations and identifying the slope and y-intercept of a line

    Standard Form

    • Equation is given by: Ax + By = C
    • A, B, and C are integers
    • A and B are not both zero
    • Useful for writing linear equations in a consistent format and solving systems of linear equations
    • Can be converted to slope-intercept form by rearranging the equation to isolate y and dividing by the coefficient of y (if necessary)

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    Description

    Learn how to solve systems of linear equations using substitution, elimination, and graphical methods. Discover the steps to find the solution to a system of equations.

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