Back to Understand that solutions to a system of two linear equations correspond to points of intersection of their graphs — Problem 2 · Task Set 33

8.EE.C.8.a Tutor Intake -- Systems of Equations, Graphical Interpretation

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Grade 8·8 problems·~8 min·Common Core Math - Grade 8·standard·8-ee-c-8a

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Concepts

Line A has slope 2.001. Line B has slope 2. On a typical graph
they look almost parallel and very close together. Does this
system have a solution?

Yes — since the slopes are different (2.001 ≠ 2), the lines must intersect at exactly one point, even if that point is far from the visible graph area.

No — the lines look so close together that they must be considered parallel with no solution.

Yes, infinitely many — lines that look this close together are essentially the same line.

It cannot be determined without graphing.