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Solving Systems of Linear Equations by Substitution quiz

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  • What is the main purpose of the substitution method when solving systems of linear equations?
    The substitution method systematically solves for one variable by substituting an expression from one equation into another, avoiding guesswork.
  • What is the first step in the substitution method?
    Choose the easiest equation to isolate x or y, and label it as equation a.
  • After choosing the easiest equation, what should you do next in the substitution method?
    Solve that equation for x or y, whichever is easier to isolate.
  • What does the substitution step involve in solving systems of equations?
    Replace the variable in the second equation with the expression found in the first equation.
  • How does substitution simplify the system of equations?
    It reduces the system to a single equation with one variable, making it easier to solve.
  • What should you do after solving for the first variable in the substitution method?
    Plug the value of the solved variable back into either original equation to find the other variable.
  • Why is it important to check your solution after using the substitution method?
    Checking ensures that the values satisfy both original equations, confirming the solution is correct.
  • What is the solution to a system of equations?
    It is a pair of values for x and y that make both equations true.
  • Why is guess and check not an efficient method for solving systems of equations?
    It can take a long time and may not yield a pair that works for both equations.
  • In the example y = 7x - 14 and 2x - y = 4, which equation is easier to isolate a variable?
    y = 7x - 14 is already isolated for y, making it the easier equation.
  • What happens to the number of variables in the equation after substitution?
    The equation is reduced to only one variable, which can then be solved directly.
  • How do you handle the minus sign when substituting expressions in equations?
    Distribute the minus sign across the substituted expression to ensure correct simplification.
  • What is the value of x in the example after substitution and solving?
    x equals 2 after solving the substituted equation.
  • How do you find the value of y after solving for x in the substitution method?
    Substitute the value of x back into the equation solved for y to find its value.
  • What are the final values of x and y in the example provided?
    x equals 2 and y equals 0, which satisfy both original equations.