일차함수와 일차방정식

Manny is making 12 quarts of orange juice from concentrate and water. The number of quarts of water is 3 times the number of quarts of concentrate. How many quarts of concentrate and how many quarts of water does Manny need?

Alisha is making an 18 ounce coffee beverage that is made from brewed coffee and milk. The number of ounces of brewed coffee is 5 times greater than the number of ounces of milk. How many ounces of coffee and how many ounces of milk does Alisha need?

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}2x-6y=0 \\ 3x-4y=5\end{array}\right.$

ⓐ $(3,1)$ ⓑ $(-3,4)$

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}7x-4y=-1 \\ -3x-2y=1\end{array}\right.$

ⓐ $(1,2)$ ⓑ $(1,-2)$

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}2x+y=5 \\ x+y=1\end{array}\right.$

ⓐ $(4,-3)$ ⓑ $(2,0)$

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}-3x+y=8 \\ -x+2y=-9\end{array}\right.$

ⓐ $(-5,-7)$ ⓑ $(-5,7)$

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.

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

ⓐ $\left(\frac{8}{7},\frac{6}{7}\right)$ ⓑ $\left(1,\frac{3}{4}\right)$

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.

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

ⓐ $\left(\frac{5}{7},\frac{2}{7}\right)$ ⓑ $(5,2)$

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}x+5y=10 \\ y=\frac{3}{5}x+1\end{array}\right.$

ⓐ $(-10,4)$ ⓑ $\left(\frac{5}{4},\frac{7}{4}\right)$

Determine Whether an Ordered Pair is a Solution of a System of Equations. In the following exercises, determine if the following points are solutions to the given system of equations.

$\left\{\begin{array}{l}x+3y=9 \\ y=\frac{2}{3}x-2\end{array}\right.$

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

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.

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

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.

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

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.

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

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.

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

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.

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

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.

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

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.

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

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.

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

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.

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

Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.

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