SAT Math Practice Question #418 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #418

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

Consider the system of linear equations below: \[ 3x - 4y = 12 \] \[ ax + by = c \] If the system has infinitely many solutions, and \( a, b, \) and \( c \) are integers such that \( a^2 + b^2 = 100 \), what is the greatest possible value of \( c \)?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

A system of equations represents geometric intersections. Consider substitution, elimination, or setting both expressions equal.

Elimination Framework (Hint 2)

Desmos Tactical Shortcut: Plot the left-hand side and right-hand side as separate equations (e.g. \( y_1 = f(x) \) and \( y_2 = g(x) \)). Click the intersection points directly to read exact coordinates.

Masterclass Solution & Distractor Trap Analysis

This question tests your conceptual understanding of systems of equations along with a bit of non-linear constraints. For a system of two linear equations to have infinitely many solutions, the two equations must represent the exact same li...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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