ACT Math Practice Question #1459 (Hard (33)) | Test Citadel
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ACT Math Difficulty: Hard (33)

Digital ACT Math Practice Question #1459

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What is the value of z in the solution to the system: x + y + z = 6, 2x - y + z = 3, and x + 2y - z = 2?
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Sum eq 1 and 3: 2x + 3y = 8. Testing x = 1, y = 2 -> 1 + 2 + z = 6 -> z = 3.

Masterclass Solution & Distractor Trap Analysis

Add eq 1 and eq 3: (x+y+z) + (x+2y-z) = 6 + 2 -> 2x + 3y = 8. Add eq 1 and eq 2: 3x + 2z = 9. Solve system: x = 1, y = 2, z = 3. Check: 1+2+3=6, 2(1)-2+3=3, 1+2(2)-3=2. All satisfy, so z = 3....

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

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