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Two-Variable Equations quiz

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  • What is the main difference between equations with one variable and equations with two variables?
    Equations with one variable have a single solution, while equations with two variables have infinitely many solutions represented as ordered pairs.
  • How do you determine if an ordered pair is a solution to a two-variable equation?
    Substitute the x and y values from the ordered pair into the equation and check if the equation is true.
  • What does it mean for a point to satisfy a two-variable equation?
    It means that when the point's x and y values are substituted into the equation, the equation holds true.
  • How are solutions to two-variable equations represented graphically?
    They are represented as points (ordered pairs) on a two-dimensional plane.
  • What is the general process for graphing a two-variable equation like -2x + y = -1?
    Isolate y, substitute various x values to find corresponding y values, plot the ordered pairs, and connect them with a line.
  • Why is it helpful to isolate y when graphing a two-variable equation?
    Isolating y makes it easier to substitute x values and directly calculate the corresponding y values.
  • What is an x-intercept and how do you find it?
    An x-intercept is where the graph crosses the x-axis, found by setting y = 0 and solving for x.
  • What is a y-intercept and how do you find it?
    A y-intercept is where the graph crosses the y-axis, found by setting x = 0 and solving for y.
  • What is always true about the y value at an x-intercept?
    The y value is always 0 at an x-intercept.
  • What is always true about the x value at a y-intercept?
    The x value is always 0 at a y-intercept.
  • If you are asked for the x-intercepts of a graph, what should you provide?
    You should provide the x values where the graph crosses the x-axis.
  • If you are asked for the intercepts of a graph (without specifying x or y), what should you provide?
    You should provide the ordered pairs where the graph crosses the axes.
  • How many ordered pairs do you typically need to plot to graph a straight line from a two-variable equation?
    Usually, 3 to 5 ordered pairs are enough to graph a straight line.
  • What happens to the graph of a two-variable equation if you plot all points that satisfy the equation?
    You get a straight line (for linear equations) that passes through all those points.
  • What does it mean if a point does not lie on the graph of a two-variable equation?
    It means the point does not satisfy the equation when its x and y values are substituted in.