연립일차방정식

For the following exercises, solve each system by elimination.

$\begin{array}{c}4x-3y+5z=31 \\ -x+2y+4z=20 \\ \,x+5y-2z=-29\end{array}$

For the following exercises, solve each system by elimination.

$\begin{array}{c}\,5x-2y+3z=4 \\ -4x+6y-7z=-1 \\ \,3x+2y-z=4\end{array}$

For the following exercises, solve each system by elimination.

$\begin{array}{c} \,4x+6y+9z=0 \\ -5x+2y-6z=3 \\ \,7x-4y+3z=-3\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\,2x-y+3z=17 \\ -5x+4y-2z=-46 \\ \,2y+5z=-7\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}5x-6y+3z=50 \\ -x+4y=10 \\ \,2x-z=10\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\,2x+3y-6z=1 \\ -4x-6y+12z=-2 \\ \,x+2y+5z=10\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\,4x+6y-2z=8 \\ \,6x+9y-3z=12 \\ -2x-3y+z=-4\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\,2x+3y-4z=5 \\ -3x+2y+z=11 \\ -x+5y+3z=4\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}10x+2y-14z=8 \\ \,-x-2y-4z=-1 \\ -12x-6y+6z=-12\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\,x+y+z=14 \\ \,2y+3z=-14 \\ -16y-24z=-112\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\,5x-3y+4z=-1 \\ -4x+2y-3z=0 \\ \,-x+5y+7z=-11\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\,x+y+z=0 \\ \,2x-y+3z=0 \\ \,x-z=0\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}3x+2y-5z=6 \\ 5x-4y+3z=-12 \\ 4x+5y-2z=15\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\,x+y+z=0 \\ 2x-y+3z=0 \\ \,x-z=1\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\begin{array}{c} \\ 3x-\frac{1}{2}y-z=-\frac{1}{2}\end{array} \\ \,4x+z=3 \\ \,-x+\frac{3}{2}y=\frac{5}{2}\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\,6x-5y+6z=38 \\ \frac{1}{5}x-\frac{1}{2}y+\frac{3}{5}z=1 \\ \,-4x-\frac{3}{2}y-z=-74\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\,\frac{1}{2}x-\frac{1}{5}y+\frac{2}{5}z=-\frac{13}{10} \\ \,\frac{1}{4}x-\frac{2}{5}y-\frac{1}{5}z=-\frac{7}{20} \\ -\frac{1}{2}x-\frac{3}{4}y-\frac{1}{2}z=-\frac{5}{4}\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}-\frac{1}{3}x-\frac{1}{2}y-\frac{1}{4}z=\frac{3}{4} \\ -\frac{1}{2}x-\frac{1}{4}y-\frac{1}{2}z=2 \\ -\frac{1}{4}x-\frac{3}{4}y-\frac{1}{2}z=-\frac{1}{2}\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\frac{1}{2}x-\frac{1}{4}y+\frac{3}{4}z=0 \\ \frac{1}{4}x-\frac{1}{10}y+\frac{2}{5}z=-2 \\ \frac{1}{8}x+\frac{1}{5}y-\frac{1}{8}z=2\end{array}$

For the following exercises, solve each system by Gaussian elimination.

$\begin{array}{c}\,\frac{4}{5}x-\frac{7}{8}y+\frac{1}{2}z=1 \\ -\frac{4}{5}x-\frac{3}{4}y+\frac{1}{3}z=-8 \\ -\frac{2}{5}x-\frac{7}{8}y+\frac{1}{2}z=-5\end{array}$