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SerloDie freie Lernplattform

Löse das Gleichungssystem mit dem Gaußverfahren.

  1. 3x+2y=−14x+y=−26x+4y=3\def\arraystretch{1.25} \begin{array}{ccrcr}3x&+&2y&=&-1\\4x&+&y&=&-2\\6x&+&4y&=&3\end{array}

  2.   x−3y=42x+y=14x+5y=9\def\arraystretch{1.25} \begin{array}{rcrcc}\;x&-&3y&=&4\\2x&+&y&=&1\\4x&+&5y&=&9\end{array}

  3. x−2y=3−2x+4y=−6  −x+2y=−3\def\arraystretch{1.25} \begin{array}{rcrcr}x&-&2y&=&3\\-2x&+&4y&=&-6\\\;-x&+&2y&=&-3\end{array}

  4. 6x−y+2z=15x−3y+3z=43x−2y+z=14\def\arraystretch{1.25} \begin{array}{rcrcrcr}6x&-&y&+&2z&=&1\\5x&-&3y&+&3z&=&4\\3x&-&2y&+&z&=&14\end{array}

  5. 34x−76y=18−9x+14y=−3213x+19y=0\def\arraystretch{1.25} \begin{array}{cccc}\frac34x&-&\frac76y&=&\frac18\\-9x&+&14y&=&-\frac32\\\frac13x&+&\frac19y&=&0\end{array}

  6. 6x−z+2y=485y−3x+3z=493z−2x+y=24\def\arraystretch{1.25} \begin{array}{rcrcrcr}6x &- & z &+ &2y &=&48\\5y &- &3x &+ &3z &=&49\\3z &- &2x &+ & y &=&24\end{array}

  7.     x−2y    =4  −y−z=−1−x+y+3z=−1\def\arraystretch{1.25} \begin{array}{rcrcrcr}\;\;x&-&2y&\;&\;&=&4\\\;&-&y&-&z&=&-1\\-x&+&y&+&3z&=&-1\end{array}

  8. 2x+3y−z=3x    +2z=9x−y    =2\def\arraystretch{1.25} \begin{array}{rcrcrcr}2x&+&3y&-&z&=&3\\x&\;&\;&+&2z&=&9\\x&-&y&\;&\;&=&2\end{array}

  9. 5x+2y−2z=−13x+y−3z=−42x    +z=4\def\arraystretch{1.25} \begin{array}{rcrcrcr}5x&+&2y&-&2z&=&-1\\3x&+&y&-&3z&=&-4\\2x&\;&\;&+&z&=&4\end{array}

  10. 4x+3y+z=132x−5y+3z=17x−y−2z=−1\def\arraystretch{1.25} \begin{array}{ccrcrcr}4x&+&3y&+&z&=&13\\2x&-&5y&+&3z&=&1\\7x&-&y&-&2z&=&-1\end{array}

  11. 2x+9y−14z=393x+6y+2z=36x2+y3+7z=2\def\arraystretch{1.25} \begin{array}{rcrcrcr}2x&+&9y&-&14z&=&39\\3x&+&6y&+&2z&=&36\\\frac x2&+&\frac y3&+&7z&=&2\end{array}

  12. x+y−z=44x−2y−2z=3−5x+4y+2z=0\def\arraystretch{1.25} \begin{array}{rcrcrcr}x&+&y&-&z&=&4\\4x&-&2y&-&2z&=&3\\-5x&+&4y&+&2z&=&0\end{array}