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{:[x_(1)+x_(2)+x_(3)=2],[2x_(1)-x_(2)+x_(3)=9],[2x_(1)+3x_(2)+4x_(3)=4]:}

x1+x2+x3=22x1−x2+x3=92x1+3x2+4x3=4 \begin{aligned} x_{1}+x_{2}+x_{3} & =2 \\ 2 x_{1}-x_{2}+x_{3} & =9 \\ 2 x_{1}+3 x_{2}+4 x_{3} & =4\end{aligned}

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Q. x1+x2+x3=22x1−x2+x3=92x1+3x2+4x3=4 \begin{aligned} x_{1}+x_{2}+x_{3} & =2 \\ 2 x_{1}-x_{2}+x_{3} & =9 \\ 2 x_{1}+3 x_{2}+4 x_{3} & =4\end{aligned}
  1. Write Equations: Step 11: Write down the system of equations.\newline{x1+x2+x3=22x1−x2+x3=92x1+3x2+4x3=4 \begin{cases} x_1 + x_2 + x_3 = 2 \\ 2x_1 - x_2 + x_3 = 9 \\ 2x_1 + 3x_2 + 4x_3 = 4 \end{cases}
  2. Elimination Method: Step 22: Use the elimination method to simplify the equations. Start by eliminating x3x_3 from the first two equations.\newlineMultiply the first equation by −1-1 and add it to the second equation:\newline−1(x1+x2+x3)+(2x1−x2+x3)=−1(2)+9 -1(x_1 + x_2 + x_3) + (2x_1 - x_2 + x_3) = -1(2) + 9 \newline−x1−x2−x3+2x1−x2+x3=−2+9 -x_1 - x_2 - x_3 + 2x_1 - x_2 + x_3 = -2 + 9 \newlinex1−2x2=7 x_1 - 2x_2 = 7

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