Back to Prove system equivalence — Problem 5 · 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

A student wants to use the REI.C.5 theorem on the system:
$E_1$ : $3x + y = 10$
$E_2$ : $x + 2y = 8$

They choose $k = -3$ and form $E_1 + (-3) \cdot E_2$ . What does the new $E_1$ become?

$3x + y - 3x - 2y = 10 - 8$ , giving $-y = 2$

$3x + y - 3(x + 2y) = 10 - 3(8)$ , giving $-5y = -14$

$3x + y - 3x - 6y = 10 - 24$ , giving $-5y = -14$

$3x + y + (-3) = 10 + (-3)$ , giving $3x + y = 7$