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How to Find the Number of Points of Intersection Given in an Algebraic Equation

If algebraic equations are not parallel to each other, they will intersect once. If an algebraic equation is intersecting with another kind of equation, such as a parabola, it can intersect with the parabola at least twice. When determining the number of points of intersection in an algebraic equation, you can either equate the algebraic equation with the other equation and solve for the solutions, which are points of intersection, or you can simply graph both and visually determine the number of intersection points.

Instructions

- 1
  Graph both the algebraic equation and the other equation in question, on an x and y coordinate system.
- 2
  Count the number of times that the algebraic equation intersects with the other equation.
- 3
  Set the two equations equal to each other, alternatively. For instance, if you want to determine the number of times x=y intersects with the circle x2+y2=4, substituting the first equation into the second leads to the equation y2+y2=4, or 2y^2=4, simplifying to y=+/- sqrt (2). Simultaneously, x will equal +/- sqrt(2), meaning that there are two possible intersection points.

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