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algebra · worked example

Solve System: 3x+2y=12 und x-y=1

Method: Einsetzungsverfahren. Verified step-by-step solution with our free AI math solver.
Problem

{3x+2y=12x−y=1\begin{cases} 3x + 2y = 12 \\ x - y = 1 \end{cases}

Step-by-step solution

  1. Löse die zweite Gleichung nach xx auf: x=y+1x = y + 1.

  2. Setze in die erste ein: 3(y+1)+2y=123(y + 1) + 2y = 12.

  3. Multipliziere aus: 3y+3+2y=123y + 3 + 2y = 12, also 5y=95y = 9.

  4. Löse: y=95y = \tfrac{9}{5}.

  5. Rücksubstitution: x=95+1=145x = \tfrac{9}{5} + 1 = \tfrac{14}{5}.

Answer

(x,y)=(145, 95)(x, y) = \bigl(\tfrac{14}{5},\ \tfrac{9}{5}\bigr)

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