SAT Math Practice Question #808 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #808

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

A system of two linear equations is shown below: \[ \frac{3}{2}x - \frac{k}{4}y = 12 \] \[ cx - 5y = 2k \] In the system above, \( c \) and \( k \) are positive constants. If the system has infinitely many solutions, what is the 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

When a system of linear equations in standard form (\( Ax + By = C \)) has infinitely many solutions, it means the two equations describe the exact same line. Therefore, their \( x \)-coefficients, \( y \)-coefficients, and constants must a...

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

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