Back to Prove system equivalence — Problem 4 · Task Set 40

Exercises: Prove That the Elimination Method Preserves Solution Sets

Work through each section in order. For proof problems, write complete logical arguments — state what you assume, what you conclude, and which properties justify each step.

Grade 9·19 problems·~40 min·Common Core Math - HS Algebra·standard·hsa-rei-c-5

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Fluency Practice

Which of the following operations on a system of two equations is legal (guaranteed to produce an equivalent system by the theorem)?

Replace $E_1$ with $E_1 + 5$ (add the constant 5 to the left side of $E_1$ )

Replace $E_1$ with $E_1 + (-2) \cdot E_2$

Replace $E_1$ with $\frac{E_1}{x}$ (divide $E_1$ by the variable $x$ )

Replace $E_1$ with $E_1^2$ (square both sides of $E_1$ )