SAT Math Practice Question #2194 (Hard) | Test Citadel
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SAT Math Difficulty: Hard

Digital SAT Math Practice Question #2194

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

In the system of equations below, the constants are unknown: $$\begin{cases} 4x - 6y = 12 \\ 2x - ky = 5 \end{cases}$$ If the system has no solution, what is the value of the constant requested?
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Socratic AI Engine Step-by-Step Derivation
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⚡ 15-Second Desmos Speed Hack

Desmos / Ratio Shortcut: For $A_1x + B_1y = C_1$ and $A_2x + B_2y = C_2$, equal slopes mean $\frac{A_1}{A_2} = \frac{B_1}{B_2}$.

Masterclass Solution & Distractor Trap Analysis

Ratio of coefficients must match for parallel lines: $\frac{4}{2} = \frac{-6}{-k} \implies 2 = \frac{6}{k} \implies k = 3$. With $k=3$, constant ratio $12/5 \ne 2$, so no solution....

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

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