여러 가지 방정식

The community college fine arts department sold three kinds of tickets to its latest dance presentation. The adult tickets sold for $20, the student tickets for $12 and the child tickets for $10.The fine arts department was thrilled to have sold 350 tickets and brought in $4,650 in one night. The number of child tickets sold is the same as the number of adult tickets sold. How many of each type did the department sell?

The community college soccer team sold three kinds of tickets to its latest game. The adult tickets sold for $10, the student tickets for $8 and the child tickets for $5. The soccer team was thrilled to have sold 600 tickets and brought in $4,900 for one game. The number of adult tickets is twice the number of child tickets. How many of each type did the soccer team sell?

Determine Whether an Ordered Triple is a Solution of a System of Three Linear Equations with Three Variables

In the following exercises, determine whether the ordered triple is a solution to the system.

$\left\{\begin{array}{l}2x-6y+z=3 \\ 3x-4y-3z=2 \\ 2x+3y-2z=3\end{array}\right.$

ⓐ $(3,1,3)$ ⓑ $(4,3,7)$

Determine Whether an Ordered Triple is a Solution of a System of Three Linear Equations with Three Variables

In the following exercises, determine whether the ordered triple is a solution to the system.

$\left\{\begin{array}{l}-3x+\,\,y+z=-4 \\ -x+2y-2z=1 \\ 2x-\,\,y-z=-1\end{array}\right.$

ⓐ $(-5,-7,4)$ ⓑ $(5,7,4)$

Determine Whether an Ordered Triple is a Solution of a System of Three Linear Equations with Three Variables

In the following exercises, determine whether the ordered triple is a solution to the system.

$\left\{\begin{array}{l}y-10z=-8 \\ 2x-y=2 \\ x-5z=3\end{array}\right.$

ⓐ $(7,12,2)$ ⓑ $(2,2,1)$

Determine Whether an Ordered Triple is a Solution of a System of Three Linear Equations with Three Variables

In the following exercises, determine whether the ordered triple is a solution to the system.

$\left\{\begin{array}{l}x+3y-z=15 \\ y=\frac{2}{3}x-2 \\ x-3y+z=-2\end{array}\right.$

ⓐ $\left(-6,5,\frac{1}{2}\right)$ ⓑ $\left(5,\frac{4}{3},-3\right)$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}5x+2y+z=5 \\ -3x-y+2z=6 \\ 2x+3y-3z=5\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}6x-5y+2z=3 \\ 2x+y-4z=5 \\ 3x-3y+z=-1\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}2x-5y+3z=8 \\ 3x-y+4z=7 \\ x+3y+2z=-3\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}5x-3y+2z=-5 \\ 2x-y-z=4 \\ 3x-2y+2z=-7\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}3x-5y+4z=5 \\ 5x+2y+z=0 \\ 2x+3y-2z=3\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}4x-3y+z=7 \\ 2x-5y-4z=3 \\ 3x-2y-2z=-7\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}3x+8y+2z=-5 \\ 2x+5y-3z=0 \\ x+2y-2z=-1\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}11x+9y+2z=-9 \\ 7x+5y+3z=-7 \\ 4x+3y+z=-3\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}\frac{1}{3}x-y-z=1 \\ x+\frac{5}{2}y+z=-2 \\ 2x+2y+\frac{1}{2}z=-4\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}x+\frac{1}{2}y+\frac{1}{2}z=0 \\ \frac{1}{5}x-\frac{1}{5}y+z=0 \\ \frac{1}{3}x-\frac{1}{3}y+2z=-1\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}x+\frac{1}{3}y-2z=-1 \\ \frac{1}{3}x+y+\frac{1}{2}z=0 \\ \frac{1}{2}x+\frac{1}{3}y-\frac{1}{2}z=-1\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}\frac{1}{3}x-y+\frac{1}{2}z=4 \\ \frac{2}{3}x+\frac{5}{2}y-4z=0 \\ x-\frac{1}{2}y+\frac{3}{2}z=2\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}x+2z=0 \\ 4y+3z=-2 \\ 2x-5y=3\end{array}\right.$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}2x+5y=4 \\ 3y-z=3 \\ 4x+3z=-3\end{array}\right.$