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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.
  • 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.
  • Why is the substitution method preferred over guessing values for x and y?
    It is systematic and avoids the inefficiency and inaccuracy of guesswork.
  • 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.
  • Once you solve for one variable, what is the next step?
    You substitute the found value back into either original equation to solve for the other variable.
  • How do you check your solution in the substitution method?
    Plug both found values into the original equations to ensure both are true.
  • In the example y = 7x - 14 and 2x - y = 4, what do you substitute for y in the second equation?
    You substitute 7x - 14 for y in the equation 2x - y = 4.
  • What is the result after substituting y = 7x - 14 into 2x - y = 4?
    The equation becomes 2x - (7x - 14) = 4.
  • How do you solve 2x - (7x - 14) = 4 for x?
    Distribute the negative sign, combine like terms, and solve for x.
  • What value of x is found in the example provided?
    x = 2.
  • After finding x = 2, how do you find y?
    Plug x = 2 into y = 7x - 14 to get y = 0.
  • What is the solution to the system y = 7x - 14 and 2x - y = 4?
    The solution is x = 2 and y = 0.
  • Why is it important to check your solution in both equations?
    To confirm that the values satisfy both equations and are correct.
  • What does it mean if your solution does not make both equations true?
    It means there was a mistake in your calculations or substitution steps.