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Lesson Plans and Worksheets for Algebra II
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Common Core For Algebra
Student Outcomes
Classwork
Opening Exercise
Find all solutions to each of the systems of equations below using any method.
2π₯ β 4π¦ = β1
3π₯ β 6π¦ = 4
π¦ = π₯2 β 2
π¦ = 2π₯ β 5
π₯2 + π¦2 = 1
π₯2 + π¦2 = 4
Exercises 1β4
Lesson Summary
An equation or a system of equations may have one or more solutions in the real numbers, or it may have no real number solution.
Two graphs that do not intersect in the coordinate plane correspond to a system of two equations without a real solution. If a system of two equations does not have a real solution, the graphs of the two equations do not intersect in the coordinate plane.
A quadratic equation in the form ππ₯2 + ππ₯ + π = 0, where π, π, and π are real numbers and π β 0, that has no real solution indicates that the graph of π¦ = ππ₯2 + ππ₯ + π does not intersect the π₯-axis.
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