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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 are considered together, and the solution is the coordinate pair(s) that satisfy all equations simultaneously.
  • How do you find the solution to a system of equations by graphing?
    You graph both equations on the same coordinate plane and identify the point where the lines intersect; this intersection point is the solution.
  • What does it mean if a point lies on both lines in a system of equations?
    It means the point is a solution to the system because it satisfies both equations at the same time.
  • What is the first step when graphing an equation not in slope-intercept form?
    Rewrite the equation in slope-intercept form (y = mx + b) to make it easier to graph.
  • How can you check if your intersection point is correct after graphing?
    Substitute the x and y values of the intersection point into both original equations to verify that both equations are true.
  • What does it mean if two lines in a system are parallel?
    If two lines are parallel, they have the same slope but different y-intercepts, so the system has no solution.
  • What does it mean if two equations in a system are actually the same line?
    If the equations are the same line, every point on the line is a solution, so there are infinitely many solutions.
  • How do you determine the number of solutions a system has without graphing?
    Write both equations in slope-intercept form and compare their slopes and y-intercepts to decide if there is one, none, or infinitely many solutions.
  • What is a consistent and independent system?
    A consistent and independent system has exactly one solution, meaning the lines intersect at one point.
  • What is a consistent and dependent system?
    A consistent and dependent system has infinitely many solutions because the equations represent the same line.
  • What is an inconsistent system of equations?
    An inconsistent system has no solutions because the lines are parallel and never intersect.
  • What does the slope represent in the equation y = mx + b?
    The slope (m) represents the steepness of the line, or how much y changes for each unit increase in x.
  • What does the y-intercept represent in the equation y = mx + b?
    The y-intercept (b) is the point where the line crosses the y-axis.
  • If two equations have different slopes, how many solutions does the system have?
    If the slopes are different, the lines will intersect at exactly one point, so there is one solution.
  • If two equations have the same slope but different y-intercepts, what does this indicate?
    This indicates the lines are parallel and the system has no solution.