Original question written by FE Exam AI Prep from the public FE Civil exam specification. Before release, a solver model re-derived the answer twice from the question alone, without its answer key, and a critic model checked the result, and the arithmetic was re-run as an executable calculation. No licensed engineer reviews these questions. It is not an NCEES question and does not come from any NCEES practice exam. FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES.
Systems of Linear Equations: FE Civil practice problem 2
For the Granite Crossing arterial overlay, a resident engineer preparing a construction-phase calculation record solves the simultaneous equations 5x + y = 16 and x - 5y = -28. What is x?
- A1.4
- B1.7
- C2.2
- D2.0
Show the answer and worked solution
Answer: D — 2.0
Worked solution
- Step 1. Set up the linear system
5x + y = 16 ; x - 5y = -28
The equations are independent because the coefficient ratios differ.
- Step 2. Eliminate y and solve for x
x = (c1*b2 - c2*b1) / (a1*b2 - a2*b1)
x = ((16)(-5) - (-28)(1)) / ((5)(-5) - (1)(1)) = -52/-26 = 2
- Step 3. Back-substitute and check
y = (c1 - a1*x) / b1
y = (16 - (5)(2)) / (1) = 6; check: (1)(2) + (-5)(6) = -28
Why the other choices are wrong
- Choice A
- Setting x = 2.4 in x - 5y = -28 requires y = 6.08, and substituting both into 5x + y = 16 produces 5(2.4) + 6.08 = 18.08 rather than 16; solving the pair by elimination instead gives x = 2.
- Choice B
- Solving x - 5y = -28 for x = 1.6 gives y = 5.92, while solving 5x + y = 16 for the same x gives y = 8; since 5.92 and 8 do not match, x = 1.6 cannot satisfy both equations, and elimination yields x = 2.
- Choice C
- Forcing x = 2.9 into 5x + y = 16 gives y = 1.5, but that pair fails x - 5y = -28 since 2.9 - 5(1.5) = -4.6 rather than -28; eliminating y from both equations directly gives x = 2.