Back to Prove system equivalence — Problem 1 · 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

Consider the system:
$E_1$ : $2x + y = 7$
$E_2$ : $x - y = 2$

The REI.C.5 theorem says we may replace $E_1$ with $E_1 + k \cdot E_2$ for any constant $k$ . If $k = 1$ , what is the new equation that replaces $E_1$ ?

$2x + y + x - y = 7$ , simplifying to $3x = 7$

$2x + y + x - y = 7 + 2$ , simplifying to $3x = 9$

$2x + y = 7 + x - y$ , giving $x + 2y = 7$

$k(x - y) = k \cdot 2$ , giving $x - y = 2$