Once students learn the strategy for doing these kinds of questions, the SAT and other standardized tests seem rather easy!

x+y=10

x^2+y^2=10

Find x^3+y^3

Ans: -350

Notes:

(1) Before giving students this question you may wish to scaffold with finding xy first.

Ans: 45

(2) To promote connection-making and to deepen their thought processes, give them the answer -350 and ask:

(a) Without graphing. explain why the graphs of the 2 given eqns DO NOT INTERSECT!

(b) Then how can there be a solution!

x+y=10

x^2+y^2=10

Find x^3+y^3

Ans: -350

Notes:

(1) Before giving students this question you may wish to scaffold with finding xy first.

Ans: 45

(2) To promote connection-making and to deepen their thought processes, give them the answer -350 and ask:

(a) Without graphing. explain why the graphs of the 2 given eqns DO NOT INTERSECT!

(b) Then how can there be a solution!

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