Question

Solve this system of three equations with three unknowns using appropriate software: $$ \begin{aligned} 2 x-y+z &=5 \\ 3 x^{2}+2 y &=z+2 \\ x y+2 z &=8 \end{aligned} $$

Short answer

Question: Using Wolfram Alpha, find the numerical solutions to the system of nonlinear equations: 2x - y + z = 5, 3x^2 + 2y = z + 2, xy + 2z = 8. Answer: There are two sets of approximate numerical solutions: 1) x ≈ 1.85108, y ≈ 1.34598, z ≈ 2.57277, and 2) x ≈ 1.14964, y ≈ 0.651957, z ≈ 2.92632.

Step-by-step solution

Access Wolfram Alpha

Go to the Wolfram Alpha website (https://www.wolframalpha.com/) to use this online software to solve the given system of equations.

Input the equations

Type or copy the following system of equations into the Wolfram Alpha search bar: "2x - y + z = 5, 3x^2 + 2y = z + 2, xy + 2z = 8" Make sure to include the commas to separate the equations, and use the caret (^) symbol for exponents.

Compute the solution

Press 'Enter' or click the magnifying glass icon to compute the solution to the system of equations.

Interpret the results

Wolfram Alpha will provide the solution to the system of nonlinear equations. In this case, we get two sets of solutions for the variables \(x\), \(y\), and \(z\): 1) \(x \approx 1.85108\), \(y \approx 1.34598\), and \(z \approx 2.57277\) 2) \(x \approx 1.14964\), \(y \approx 0.651957\), and \(z \approx 2.92632\) These are the two sets of approximate numerical values that satisfy all three equations in the given system.