Question

Solve the following systems of linear

(a). x₁ - x₂ + 2x₃ = 2
2x₂ + x₃ = 4
2x₁ + 4x₃ = 1.

Answer 1

To solve the given system of linear equations, use substitution and elimination starting with equation (2), then proceed with substituting values from one equation into the others, and solve step-by-step to find the values for x1, x2, and x3.

Step-by-step explanation:

To solve the simultaneous equations for the unknowns x1, x2, and x3, we'll follow a systematic approach of substitution and elimination. First, let's arrange the given equations:

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Now we isolate x2 in equation (2):

x2 = (4 - x3)/2

Then, we substitute this expression of x2 into equation (1), which allows us to find x1:

x1 = (2 + x2 - 2x3)

Substituting x2 from equation (2) and solving for x1 will give us a value that we can then use with equation (3) to find x3. Finally, we will be able to back-substitute these values to find the remaining unknowns. Algebraic steps with careful checking and rechecking are needed throughout this process.