방정식과 부등식 전체 문제

For the following exercises, use Gaussian elimination to solve the systems of equations.

$\begin{array}{c}x-6y=4 \\ 2x-12y=0\end{array}$

For the following exercises, use Gaussian elimination to solve the systems of equations.

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

For the following exercises, use the inverse of a matrix to solve the systems of equations.

$\begin{array}{c}4x-5y=-50 \\ -x+2y=80\end{array}$

For the following exercises, use the inverse of a matrix to solve the systems of equations.

$\begin{array}{c}\frac{1}{100}x-\frac{3}{100}y+\frac{1}{20}z=-49 \\ \frac{3}{100}x-\frac{7}{100}y-\frac{1}{100}z=13 \\ \frac{9}{100}x-\frac{9}{100}y-\frac{9}{100}z=99\end{array}$

For the following exercises, use Cramer’s Rule to solve the systems of equations.

$\begin{array}{c}200x-300y=2 \\ 400x+715y=4\end{array}$

For the following exercises, use Cramer’s Rule to solve the systems of equations.

$\begin{array}{c}0.1x+0.1y-0.1z=-1.2 \\ 0.1x-0.2y+0.4z=-1.2 \\ 0.5x-0.3y+0.8z=-5.9\end{array}$

For the following exercises, solve using a system of linear equations.

A factory producing cell phones has the following cost and revenue functions: $C(x)={x}^{2}+75x+2,688$ and $R(x)={x}^{2}+160x.$ What is the range of cell phones they should produce each day so there is profit? Round to the nearest number that generates profit.

For the following exercises, solve using a system of linear equations.

A small fair charges $1.50 for students, $1 for children, and $2 for adults. In one day, three times as many children as adults attended. A total of 800 tickets were sold for a total revenue of $1,050. How many of each type of ticket was sold?