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{:[3I_(1)-I_(2)+3I_(3)+2I_(4)=12],[I_(1)-2I_(3)+I_(4)=-1],[5I_(1)-5I_(2)+I_(3)+2I_(4)=8],[3I_(1)+I_(2)+2I_(3)+2I_(4)=10],[I_(1)=iI_(1)]:}

3I1I2+3I3+2I4=12I12I3+I4=15I15I2+I3+2I4=83I1+I2+2I3+2I4=10I1=iI1 \begin{array}{r}3 I_{1}-I_{2}+3 I_{3}+2 I_{4}=12 \\ I_{1}-2 I_{3}+I_{4}=-1 \\ 5 I_{1}-5 I_{2}+I_{3}+2 I_{4}=8 \\ 3 I_{1}+I_{2}+2 I_{3}+2 I_{4}=10 \\ I_{1}=\mathbf{i} I_{1}\end{array}

Full solution

Q. 3I1I2+3I3+2I4=12I12I3+I4=15I15I2+I3+2I4=83I1+I2+2I3+2I4=10I1=iI1 \begin{array}{r}3 I_{1}-I_{2}+3 I_{3}+2 I_{4}=12 \\ I_{1}-2 I_{3}+I_{4}=-1 \\ 5 I_{1}-5 I_{2}+I_{3}+2 I_{4}=8 \\ 3 I_{1}+I_{2}+2 I_{3}+2 I_{4}=10 \\ I_{1}=\mathbf{i} I_{1}\end{array}
  1. Write Equations: Write down the system of equations. {3I1I2+3I3+2I4=12, I12I3+I4=1, 5I15I2+I3+2I4=8, 3I1+I2+2I3+2I4=10, I1=iI1\begin{cases} 3I_1-I_2+3I_3+2I_4=12, \ I_1-2I_3+I_4=-1, \ 5I_1-5I_2+I_3+2I_4=8, \ 3I_1+I_2+2I_3+2I_4=10, \ I_1=iI_1 \end{cases}
  2. Simplify Equation: Simplify the last equation.\newlineThe last equation I1=iI1I_{1}=iI_{1} doesn't make sense, it implies I1=0I_{1} = 0 or it's a typo. We can't solve for imaginary numbers in this context, so we'll ignore this equation.

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