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 1
For the Stone Yard concrete-lined channel, a hydrology reviewer preparing an operations handoff review solves the simultaneous equations 5x + 4y = 65 and x - 5y = -16. What is x?
- A6.1
- B7.6
- C9.0
- D9.8
Show the answer and worked solution
Answer: C — 9.0
Worked solution
- Step 1. Set up the linear system
5x + 4y = 65 ; x - 5y = -16
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 = ((65)(-5) - (-16)(4)) / ((5)(-5) - (1)(4)) = -261/-29 = 9
- Step 3. Back-substitute and check
y = (c1 - a1*x) / b1
y = (65 - (5)(9)) / (4) = 5; check: (1)(9) + (-5)(5) = -16
Why the other choices are wrong
- Choice A
- This number equals the true solution x of 9.0 multiplied by roughly 0.78 instead of evaluating x = (c1 * b2 - c2 * b1) / (a1 * b2 - a2 * b1) for this pair of equations, so substituting it back fails both equations.
- Choice B
- This answer equals the correct value of x of 9.0 multiplied by close to 1.45, a scale-up that does not come from any single elimination step in x = (c1 * b2 - c2 * b1) / (a1 * b2 - a2 * b1), so it does not solve the given system.
- Choice D
- This value equals the correctly eliminated x of 9.0 multiplied by about 1.18 rather than being computed from x = (c1 * b2 - c2 * b1) / (a1 * b2 - a2 * b1) using the stated coefficients, so it fails to satisfy either equation in the system.