방정식과 부등식 전체 문제

For the following exercises, solve the system of three equations using substitution or addition.

$\begin{array}{c}5x+3y-z=5 \\ 3x-2y+4z=13 \\ 4x+3y+5z=22\end{array}$

For the following exercises, solve the system of three equations using substitution or addition.

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

For the following exercises, solve the system of three equations using substitution or addition.

$\begin{array}{c}2x-3y+z=-1 \\ x+y+z=-4 \\ 4x+2y-3z=33\end{array}$

For the following exercises, solve the system of three equations using substitution or addition.

$\begin{array}{c}3x+2y-z=-10 \\ x-y+2z=7 \\ -x+3y+z=-2\end{array}$

For the following exercises, solve the system of three equations using substitution or addition.

$\begin{array}{c}3x+4z=-11 \\ x-2y=5 \\ 4y-z=-10\end{array}$

For the following exercises, solve the system of three equations using substitution or addition.

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

For the following exercises, solve the system of three equations using substitution or addition.

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

For the following exercises, write a system of equations to solve each problem. Solve the system of equations.

Three odd numbers sum up to 61. The smaller is one-third the larger and the middle number is 16 less than the larger. What are the three numbers?

For the following exercises, write a system of equations to solve each problem. Solve the system of equations.

A local theatre sells out for their show. They sell all 500 tickets for a total purse of $8,070.00. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children’s tickets, how many of each type was sold?

Is the following ordered pair a solution to the system of equations?

$\begin{array}{c} \\ \begin{array}{c}-5x-y=12 \\ x+4y=9\end{array}\end{array}$ with $(-3,3)$

For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists.

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

For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists.

$\begin{array}{c} \\ -\frac{1}{2}x-4y=4 \\ 2x+16y=2\end{array}$

For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists.

$\begin{array}{c}5x-y=1 \\ -10x+2y=-2\end{array}$

For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists.

$\begin{array}{c}4x-6y-2z=\frac{1}{10} \\ x-7y+5z=-\frac{1}{4} \\ 3x+6y-9z=\frac{6}{5}\end{array}$

For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists.

$\begin{array}{c}x+z=20 \\ x+y+z=20 \\ x+2y+z=10\end{array}$

For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists.

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

For the following exercises, solve the systems of linear and nonlinear equations using substitution or elimination. Indicate if no solution exists.

$\begin{array}{c}{y}^{2}+{x}^{2}=25 \\ {y}^{2}-2{x}^{2}=1\end{array}$

For the following exercises, write the partial fraction decomposition.

$\frac{-8x-30}{{x}^{2}+10x+25}$

For the following exercises, write the partial fraction decomposition.

$\frac{13x+2}{{(3x+1)}^{2}}$

For the following exercises, write the partial fraction decomposition.

$\frac{{x}^{4}-{x}^{3}+2x-1}{x{({x}^{2}+1)}^{2}}$