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Solving Systems of Linear Equations by Substitution quiz

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  • What is the main goal when solving a system of equations using the substitution method?
    The main goal is to find values for x and y that make both equations true by substituting one equation into the other.
  • Why might the guess and check method be inefficient for solving systems of equations?
    Guess and check can take a long time because you might find values that work for one equation but not both.
  • What is the first step in the substitution method?
    The first step is to choose the easiest equation to isolate x or y.
  • After isolating a variable in one equation, what do you do next in the substitution method?
    You substitute the isolated variable's expression into the other equation.
  • What happens to the number of variables in the equation after substitution?
    After substitution, the equation has only one variable, making it easier to solve.
  • How do you solve for the second variable after finding the first variable's value?
    You substitute the value of the first variable back into either original equation to solve for the second variable.
  • Why is it important to check your solution in both equations?
    Checking ensures that your solution makes both equations true, confirming its correctness.
  • In the example y = 7x - 14 and 2x - y = 4, what is the value of x after substitution and solving?
    The value of x is 2.
  • Using the same example, what is the value of y after substituting x = 2?
    The value of y is 0.
  • What does it mean to 'isolate' a variable in an equation?
    To isolate a variable means to solve the equation so that the variable is alone on one side.
  • What should you do if both equations are already solved for a variable?
    You can choose either equation to substitute into the other.
  • What is the purpose of distributing the negative sign when substituting expressions?
    Distributing the negative sign ensures correct simplification of the equation.
  • What does a solution to a system of equations represent?
    It represents the values of x and y that make both equations true at the same time.
  • What is the final step in the substitution method?
    The final step is to check your solution by plugging the values into both original equations.
  • Why does the substitution method avoid guesswork?
    Because it uses a systematic process to find the exact solution without trial and error.