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  1. Home
  2. 12th grade
  3. Algebra I
  4. Exercise : Convert a system of equations into a triangular system

Convert a system of equations into a triangular system Algebra I

Find a triangular system that is equivalent to the following systems, using elementary row operations.

\begin{cases} x+3y-z=2 \cr \cr 3x+2y+3z=4 \cr \cr x+y-z=2 \end{cases}

\begin{cases} 2x-3y=2 \cr \cr x+2y=5 \end{cases}

\begin{cases} x-4y=9 \cr \cr 3x+8y=7 \end{cases}

\begin{cases} 2x+5y=3 \cr \cr 3x+4y=-1 \end{cases}

\begin{cases} x+y-z=2 \cr \cr 2x+2y+3z=7 \cr \cr 3x-y-2z=0 \end{cases}

\begin{cases} x-z=2 \cr \cr x+y=4 \cr \cr y-z=-2 \end{cases}

\begin{cases} x+y+z=5 \cr \cr 2x+2y+3z=10 \cr \cr 4x-5y+z=2 \end{cases}

See also
  • Course : System of linear equations
  • Exercise : Convert a word problem into a system of linear equations
  • Exercise : Solve a system of equation using substitution
  • Exercise : Solve a system of equation using elimination
  • Exercise : Solve a system of equation using the Gaussian elimination
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