연립일차방정식

For the following exercises, use substitution to solve the system of equations.

$\begin{array}{c}\frac{4}{7}x+\frac{1}{5}y=\frac{43}{70} \\ \frac{5}{6}x-\frac{1}{3}y=-\frac{2}{3}\end{array}$

For the following exercises, use substitution to solve the system of equations.

$\begin{array}{c}5x+6y=14 \\ 4x+8y=8\end{array}$

For the following exercises, use addition to solve the system of equations.

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

For the following exercises, use addition to solve the system of equations.

$\begin{array}{c}3x+4y=2 \\ 9x+12y=3\end{array}$

For the following exercises, use addition to solve the system of equations.

$\begin{array}{c}8x+4y=2 \\ 6x-5y=0.7\end{array}$

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

A factory has a cost of production $C(x)=150x+15,000$ and a revenue function $R(x)=200x.$ What is the break-even point?

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

A performer charges $C(x)=50x+10,000,$ where $x$ is the total number of attendees at a show. The venue charges $75 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?

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

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

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?