방정식과 부등식 전체 문제

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?

Three numbers sum up to 147. The smallest number is half the middle number, which is half the largest number. What are the three numbers?

At a family reunion, there were only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and grandparents were in attendance?

An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one-half the number of cats, and there are 20 more cats than dogs, how many of each animal are at the shelter?

Your roommate, Shani, offered to buy groceries for you and your other roommate. The total bill was $82. She forgot to save the individual receipts but remembered that your groceries were $0.05 cheaper than half of her groceries, and that your other roommate’s groceries were $2.10 more than your groceries. How much was each of your share of the groceries?