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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 x, y pairs that satisfy all equations.
  • How do you determine if a point is a solution to a single linear equation graphically?
    A point is a solution if it lies on the line when the equation is graphed.
  • What does it mean for a point to be a solution to a system of equations?
    The point must satisfy all equations in the system, meaning it lies on all lines when graphed.
  • What is the graphical solution to a system of two linear equations?
    The solution is the intersection point of the two lines on the graph.
  • How do you graph an equation in slope-intercept form?
    Start at the y-intercept and use the slope to find additional points, then connect them with a straight line.
  • What should you do if an equation is not in slope-intercept form before graphing?
    Rewrite the equation in y = mx + b form by isolating y.
  • How can you check your solution after graphing a system of equations?
    Plug the intersection point's x and y values into both equations to verify they make true statements.
  • What does it mean if two lines are parallel when graphed?
    Parallel lines never intersect, so the system has no solution.
  • What happens if two equations in a system are actually the same line?
    There are infinitely many solutions because every point on the line satisfies both equations.
  • How can you determine the number of solutions to a system without graphing?
    Write both equations in y = mx + b form and compare their slopes and y-intercepts.
  • What does it mean if the slopes of two equations are different?
    The lines will intersect at one point, so the system has exactly one solution.
  • What does it mean if the slopes are the same but the y-intercepts are different?
    The lines are parallel and the system has zero solutions.
  • What does it mean if both the slopes and y-intercepts are the same for two equations?
    The equations represent the same line, so there are infinitely many solutions.
  • What is a consistent and independent system of equations?
    It is a system with exactly one solution, where the lines intersect at a single point.
  • What is an inconsistent system of equations?
    It is a system with no solution, usually because the lines are parallel and never intersect.