Question

Solve the following simultaneous equations:


`\displaystyle{\begin{cases}2x_1+x_2+x_3+x_4+x_5 = 6 \\ x_1+2x_2+x_3+x_4+x_5 = 12 \\ x_1+x_2+2x_3+x_4+x_5=24\\ x_1+x_2+x_3+2x_4+x_5=48 \\ x_1+x_2+x_3+x_4+2x_5 = 96\end{cases}}`

Answer 1

First step, let's call the sum of all unknowns as k.

Then the system becomes:

• 
  `x_1+k=6`
• 
  `x_2+k=12`
• 
  `x_3+k=24`
• 
  `x_4+k=48`
• 
  `x_5+k=96`

Second step, add up all equations to get:

• k + 5k = 6 + 12 + 24 + 48 + 96
• 6k = 186
• k = 31

Last step, substitute the value of k back into secondary equations and find each unknown:

• x₁ = - 25
• x₂ = - 19
• x₃ = - 7
• x₄ = 17
• x₅ = 65