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Solving Systems of Linear Equations by Graphing quiz

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  • What is a system of linear equations?
    A system of linear equations is a set of two or more linear equations that you solve simultaneously to find coordinate pairs that satisfy all equations.
  • How do you graph a linear equation in slope-intercept form?
    Start by plotting the y-intercept, then use the slope to find additional points, and connect them with a straight line.
  • What does the intersection point of two lines represent when solving a system by graphing?
    The intersection point is the solution to the system, as it satisfies both equations simultaneously.
  • How do you convert an equation from standard form to slope-intercept form?
    Isolate y by moving other terms to the opposite side and rearrange to get y = mx + b.
  • What should you do after finding the intersection point when solving by graphing?
    Plug the x and y values of the intersection point into both equations to check if they make true statements.
  • What does it mean if two lines are parallel when graphing a system?
    Parallel lines have the same slope but different y-intercepts, so they never intersect and the system has zero solutions.
  • What happens if two equations graph as the same line?
    If the lines are identical, every point on the line is a solution, so the system has infinitely many solutions.
  • How can you determine the number of solutions without graphing?
    Write both equations in y = mx + b form and compare their slopes and y-intercepts.
  • What does it mean if two equations have different slopes?
    Different slopes mean the lines will intersect at one point, so the system has exactly one solution.
  • What does it mean if two equations have the same slope but different y-intercepts?
    Same slopes and different y-intercepts indicate parallel lines, resulting in zero solutions.
  • What does it mean if two equations have the same slope and same y-intercept?
    Same slope and y-intercept means the lines are identical, so there are infinitely many solutions.
  • What is a consistent and independent system?
    A consistent and independent system has one solution, meaning the lines intersect at a single point.
  • What is a consistent and dependent system?
    A consistent and dependent system has infinitely many solutions, meaning the lines are the same.
  • What is an inconsistent system?
    An inconsistent system has zero solutions, meaning the lines are parallel and never intersect.
  • Why is it important to check your solution after graphing?
    Checking ensures the intersection point actually satisfies both equations, especially if the graph was drawn by hand and may be imprecise.