<< Chapter < Page | Chapter >> Page > |
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?
Manny needs 3 quarts juice concentrate and 9 quarts water.
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?
Alisha needs 15 ounces of coffee and 3 ounces of milk.
Access these online resources for additional instruction and practice with solving systems of equations by graphing.
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.
$\{\begin{array}{c}2x-6y=0\hfill \\ 3x-4y=5\hfill \end{array}$
ⓐ $(3,1)$ ⓑ $(\mathrm{-3},4)$
ⓐ yes ⓑ no
$\{\begin{array}{c}7x-4y=\mathrm{-1}\hfill \\ \mathrm{-3}x-2y=1\hfill \end{array}$
ⓐ ⓑ $(1,\mathrm{-2})$
$\{\begin{array}{c}2x+y=5\hfill \\ x+y=1\hfill \end{array}$
ⓐ $(4,\text{\u22123})$ ⓑ $(2,0)$
ⓐ yes ⓑ no
$\{\begin{array}{c}\mathrm{-3}x+y=8\hfill \\ -x+2y=\mathrm{-9}\hfill \end{array}$
ⓐ $(\mathrm{-5},\mathrm{-7})$ ⓑ $(\mathrm{-5},7)$
$\{\begin{array}{c}x+y=2\hfill \\ y=\frac{3}{4}x\hfill \end{array}$
ⓐ $\left(\frac{8}{7},\frac{6}{7}\right)$ ⓑ $\left(1,\frac{3}{4}\right)$
ⓐ yes ⓑ no
$\{\begin{array}{c}x+y=1\hfill \\ y=\frac{2}{5}x\hfill \end{array}$
ⓐ $\left(\frac{5}{7},\frac{2}{7}\right)$ ⓑ $\left(5,2\right)$
$\{\begin{array}{c}x+5y=10\hfill \\ y=\frac{3}{5}x+1\hfill \end{array}$
ⓐ $\left(\mathrm{-10},4\right)$ ⓑ $\left(\frac{5}{4},\frac{7}{4}\right)$
ⓐ no ⓑ yes
$\{\begin{array}{c}x+3y=9\hfill \\ y=\frac{2}{3}x-2\hfill \end{array}$
ⓐ $\left(\mathrm{-6},5\right)$ ⓑ $\left(5,\frac{4}{3}\right)$
Solve a System of Linear Equations by Graphing In the following exercises, solve the following systems of equations by graphing.
$\{\begin{array}{c}3x+y=\mathrm{-3}\hfill \\ 2x+3y=5\hfill \end{array}$
$(\mathrm{-2},3)$
$\{\begin{array}{c}\text{\u2212}x+y=2\hfill \\ 2x+y=\mathrm{-4}\hfill \end{array}$
$\{\begin{array}{c}\mathrm{-3}x+y=\mathrm{-1}\hfill \\ 2x+y=4\hfill \end{array}$
$\left(1,2\right)$
$\{\begin{array}{c}\mathrm{-2}x+3y=\mathrm{-3}\hfill \\ x+y=4\hfill \end{array}$
$\{\begin{array}{c}y=x+2\hfill \\ y=\mathrm{-2}x+2\hfill \end{array}$
$(0,2)$
$\{\begin{array}{c}y=x-2\hfill \\ y=\mathrm{-3}x+2\hfill \end{array}$
$\{\begin{array}{c}y=\frac{3}{2}x+1\hfill \\ y=-\frac{1}{2}x+5\hfill \end{array}$
$(2,4)$
$\{\begin{array}{c}y=\frac{2}{3}x-2\hfill \\ y=-\frac{1}{3}x-5\hfill \end{array}$
$\{\begin{array}{c}-x+y=\mathrm{-3}\hfill \\ 4x+4y=4\hfill \end{array}$
$(2,\mathrm{-1})$
$\{\begin{array}{c}x-y=3\hfill \\ 2x-y=4\hfill \end{array}$
$\{\begin{array}{c}\mathrm{-3}x+y=\mathrm{-1}\hfill \\ 2x+y=4\hfill \end{array}$
$(1,2)$
$\{\begin{array}{c}\mathrm{-3}x+y=\mathrm{-2}\hfill \\ 4x-2y=6\hfill \end{array}$
$\{\begin{array}{c}x+y=5\hfill \\ 2x-y=4\hfill \end{array}$
$(3,2)$
$\{\begin{array}{c}x-y=2\hfill \\ 2x-y=6\hfill \end{array}$
$\{\begin{array}{c}x+y=2\hfill \\ x-y=0\hfill \end{array}$
$(1,1)$
$\{\begin{array}{c}x+y=6\hfill \\ x-y=\mathrm{-8}\hfill \end{array}$
$\{\begin{array}{c}x+y=\mathrm{-5}\hfill \\ x-y=3\hfill \end{array}$
$(\mathrm{-1},\mathrm{-4})$
$\{\begin{array}{c}x+y=4\hfill \\ x-y=0\hfill \end{array}$
$\{\begin{array}{c}x+y=\mathrm{-4}\hfill \\ -x+2y=\mathrm{-2}\hfill \end{array}$
$(3,3)$
$\{\begin{array}{c}-x+3y=3\hfill \\ x+3y=3\hfill \end{array}$
$\{\begin{array}{c}\mathrm{-2}x+3y=3\hfill \\ x+3y=12\hfill \end{array}$
$(\mathrm{-5},6)$
$\{\begin{array}{c}2x-y=4\hfill \\ 2x+3y=12\hfill \end{array}$
$\{\begin{array}{c}2x+3y=6\hfill \\ y=\mathrm{-2}\hfill \end{array}$
$(6,\mathrm{-2})$
Notification Switch
Would you like to follow the 'Elementary algebra' conversation and receive update notifications?