An interesting pair of simultaneous equations

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In this teacher presentation and collection of student worksheets a pair of simultaneous equations is given, one of which is non-linear. A second pair of similar simultaneous equations is given; that has the same solutions. Students are challenged to explain why.

Each student worksheet contains different pairs of simultaneous equations, but for each the solutions all have something in common.

The teacher presentation includes a graphical solution to explain how the solution works.

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