use a computer software or graphing utility to solve the system of linear equation.
x₁+0.5x₂+0.33x₃+0.25x₄=1.1
0.5x₁+0.33x₂+0.25x₃+0.21x₄=1.2
0.33x₁+0.25x₂+0.2x₃+0.17x₄=1.3
0.25x₁+0.2x₂+0.17x₃+0.14x₄=1.4
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To solve this system of linear equations using a computer software or graphing utility, you can follow these steps:
Step 1: Input the equations into the software or graphing utility:
Enter the coefficients and constants of each equation into the software. In this case, you have four equations with four variables (x₁, x₂, x₃, and x₄), so enter the following equations:
Equation 1: x₁ + 0.5x₂ + 0.33x₃ + 0.25x₄ = 1.1
Equation 2: 0.5x₁ + 0.33x₂ + 0.25x₃ + 0.21x₄ = 1.2
Equation 3: 0.33x₁ + 0.25x₂ + 0.2x₃ + 0.17x₄ = 1.3
Equation 4: 0.25x₁ + 0.2x₂ + 0.17x₃ + 0.14x₄ = 1.4
Step 2: Solve the system:
Click on the "solve" or "calculate" button in the software or graphing utility. The software will use various mathematical methods, such as Gaussian elimination or matrix operations, to find the solution.
Step 3: Interpret the result:
The software or graphing utility will display the solution to the system of linear equations. It will provide the values of x₁, x₂, x₃, and x₄ that satisfy all four equations simultaneously.
That's it! By following these steps, you can use a computer software or graphing utility to solve the given system of linear equations.