방정식과 부등식 전체 문제

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.

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

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

$\begin{array}{c} \\ -\frac{1}{3}x-\frac{1}{8}y+\frac{1}{6}z=-\frac{4}{3} \\ -\frac{2}{3}x-\frac{7}{8}y+\frac{1}{3}z=-\frac{23}{3} \\ -\frac{1}{3}x-\frac{5}{8}y+\frac{5}{6}z=0\end{array}$

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

$\begin{array}{c} \\ -\frac{1}{4}x-\frac{5}{4}y+\frac{5}{2}z=-5 \\ -\frac{1}{2}x-\frac{5}{3}y+\frac{5}{4}z=\frac{55}{12} \\ -\frac{1}{3}x-\frac{1}{3}y+\frac{1}{3}z=\frac{5}{3}\end{array}$

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

$\begin{array}{c}\frac{1}{40}x+\frac{1}{60}y+\frac{1}{80}z=\frac{1}{100} \\ \,-\frac{1}{2}x-\frac{1}{3}y-\frac{1}{4}z=-\frac{1}{5} \\ \,\frac{3}{8}x+\frac{3}{12}y+\frac{3}{16}z=\frac{3}{20}\end{array}$

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

$\begin{array}{c}0.1x-0.2y+0.3z=2 \\ 0.5x-0.1y+0.4z=8 \\ 0.7x-0.2y+0.3z=8\end{array}$

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

$\begin{array}{c}0.2x+0.1y-0.3z=0.2 \\ 0.8x+0.4y-1.2z=0.1 \\ 1.6x+0.8y-2.4z=0.2\end{array}$

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

$\begin{array}{c}1.1x+0.7y-3.1z=-1.79 \\ 2.1x+0.5y-1.6z=-0.13 \\ 0.5x+0.4y-0.5z=-0.07\end{array}$

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

$\begin{array}{c}0.5x-0.5y+0.5z=10 \\ 0.2x-0.2y+0.2z=4 \\ 0.1x-0.1y+0.1z=2\end{array}$

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

$\begin{array}{c}0.1x+0.2y+0.3z=0.37 \\ 0.1x-0.2y-0.3z=-0.27 \\ 0.5x-0.1y-0.3z=-0.03\end{array}$

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

$\begin{array}{c}0.5x-0.5y-0.3z=0.13 \\ 0.4x-0.1y-0.3z=0.11 \\ 0.2x-0.8y-0.9z=-0.32\end{array}$

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

$\begin{array}{c}0.5x+0.2y-0.3z=1 \\ 0.4x-0.6y+0.7z=0.8 \\ 0.3x-0.1y-0.9z=0.6\end{array}$

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

$\begin{array}{c}0.3x+0.3y+0.5z=0.6 \\ 0.4x+0.4y+0.4z=1.8 \\ 0.4x+0.2y+0.1z=1.6\end{array}$

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

$\begin{array}{c}0.8x+0.8y+0.8z=2.4 \\ 0.3x-0.5y+0.2z=0 \\ 0.1x+0.2y+0.3z=0.6\end{array}$

For the following exercises, solve the system for $x,y,$ and $z.$

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

For the following exercises, solve the system for $x,y,$ and $z.$

$\begin{array}{c}5x-3y-\frac{z+1}{2}=\frac{1}{2} \\ 6x+\frac{y-9}{2}+2z=-3 \\ \,\frac{x+8}{2}-4y+z=4\end{array}$

For the following exercises, solve the system for $x,y,$ and $z.$

$\begin{array}{c}\frac{x+4}{7}-\frac{y-1}{6}+\frac{z+2}{3}=1 \\ \frac{x-2}{4}+\frac{y+1}{8}-\frac{z+8}{12}=0 \\ \frac{x+6}{3}-\frac{y+2}{3}+\frac{z+4}{2}=3\end{array}$

For the following exercises, solve the system for $x,y,$ and $z.$

$\begin{array}{c}\frac{x-3}{6}+\frac{y+2}{2}-\frac{z-3}{3}=2 \\ \frac{x+2}{4}+\frac{y-5}{2}+\frac{z+4}{2}=1 \\ \frac{x+6}{2}-\frac{y-3}{2}+z+1=9\end{array}$

For the following exercises, solve the system for $x,y,$ and $z.$

$\begin{array}{c}\,\frac{x-1}{3}+\frac{y+3}{4}+\frac{z+2}{6}=1 \\ \,4x+3y-2z=11 \\ 0.02x+0.015y-0.01z=0.065\end{array}$

Three even numbers sum up to 108. The smaller is half the larger and the middle number is $\frac{3}{4}$

the larger. What are the three numbers?