Find all solutions to each of the systems of equations below using any method.
2𝑥 − 4𝑦 = −1
3𝑥 − 6𝑦 = 4
𝑦 = 𝑥2 − 2
𝑦 = 2𝑥 − 5
𝑥2 + 𝑦2 = 1
𝑥2 + 𝑦2 = 4
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 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0, where 𝑎, 𝑏, and 𝑐 are real numbers and 𝑎 ≠ 0, that has no real solution indicates that the graph of 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐 does not intersect the 𝑥-axis.
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