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Two Variable Systems of Linear Equations quiz

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  • What is a system of equations?
    A system of equations is a set of two or more equations with the same variables, which must be solved simultaneously.
  • What does it mean for a point to be a solution to a system of equations?
    A point is a solution if it satisfies all equations in the system at the same time.
  • How can you check if a point is a solution to a single linear equation graphically?
    If the point lies on the line represented by the equation, it is a solution.
  • What is the graphical interpretation of the solution to a system of two linear equations?
    The solution is the point where the two lines intersect on the graph.
  • What are the three methods commonly used to solve systems of linear equations?
    The three methods are graphing, substitution, and elimination.
  • What is the first step in the substitution method?
    Isolate one variable in one of the equations, making it easy to substitute.
  • After substituting one equation into another in the substitution method, what do you do next?
    Solve the resulting equation for the remaining variable.
  • How do you find the value of the second variable after using substitution?
    Plug the value of the first variable back into either original equation and solve.
  • What is the elimination method designed to do?
    The elimination method is designed to add or subtract equations to eliminate one variable.
  • When using elimination, what must you do if the coefficients are not equal and opposite?
    Multiply one or both equations by suitable numbers to make the coefficients equal and opposite.
  • What happens if all variables cancel out and you are left with a true statement in a system?
    This means the system has infinitely many solutions and the lines are identical (dependent system).
  • What does it mean if all variables cancel and you are left with a false statement?
    It means the system has no solution and the lines are parallel (inconsistent system).
  • What is a consistent independent system?
    A consistent independent system has exactly one solution, where the lines intersect at a single point.
  • What is a consistent dependent system?
    A consistent dependent system has infinitely many solutions because the lines are identical.
  • What is an inconsistent system?
    An inconsistent system has no solutions because the lines are parallel and never intersect.