5.6 Graphing systems of linear inequalities  (Page 7/10)

$\{\begin{array}{c}3x+y=6\hfill \\ x+3y=\mathrm{-6}\hfill \end{array}$

$\{\begin{array}{c}y=x-2\hfill \\ y=\mathrm{-2}x-2\hfill \end{array}$

$\{\begin{array}{c}2x-y=6\hfill \\ y=4\hfill \end{array}$

$\{\begin{array}{c}x+4y=\mathrm{-1}\hfill \\ x=3\hfill \end{array}$

$\{\begin{array}{c}2x-y=5\hfill \\ 4x-2y=10\hfill \end{array}$

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

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

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

$\{\begin{array}{c}5x-4y=0\hfill \\ y=\frac{5}{4}x-5\hfill \end{array}$

$\{\begin{array}{c}y=-\frac{3}{4}x+1\hfill \\ 6x+8y=8\hfill \end{array}$

LaVelle is making a pitcher of caffe mocha. For each ounce of chocolate syrup, she uses five ounces of coffee. How many ounces of chocolate syrup and how many ounces of coffee does she need to make 48 ounces of caffe mocha?

Eli is making a party mix that contains pretzels and chex. For each cup of pretzels, he uses three cups of chex. How many cups of pretzels and how many cups of chex does he need to make 12 cups of party mix?

$\{\begin{array}{c}3x-y=\mathrm{-5}\hfill \\ y=2x+4\hfill \end{array}$

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

$\{\begin{array}{c}x-y=0\hfill \\ 2x+5y=\mathrm{-14}\hfill \end{array}$

$\{\begin{array}{c}y=\mathrm{-2}x+7\hfill \\ y=\frac{2}{3}x-1\hfill \end{array}$

$\{\begin{array}{c}y=\mathrm{-5}x\hfill \\ 5x+y=6\hfill \end{array}$

$\{\begin{array}{c}y=-\frac{1}{3}x+2\hfill \\ x+3y=6\hfill \end{array}$

The sum of two number is 55. One number is 11 less than the other. Find the numbers.

The perimeter of a rectangle is 128. The length is 16 more than the width. Find the length and width.

The measure of one of the small angles of a right triangle is 2 less than 3 times the measure of the other small angle. Find the measure of both angles.

Gabriela works for an insurance company that pays her a salary of $32,000 plus a commission of $100 for each policy she sells. She is considering changing jobs to a company that would pay a salary of $40,000 plus a commission of $80 for each policy sold. How many policies would Gabriela need to sell to make the total pay the same?

$\{\begin{array}{c}x+y=12\hfill \\ x-y=\mathrm{-10}\hfill \end{array}$

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

$\{\begin{array}{c}3x-8y=20\hfill \\ x+3y=1\hfill \end{array}$

$\{\begin{array}{c}3x-2y=6\hfill \\ 4x+3y=8\hfill \end{array}$

$\{\begin{array}{c}9x+4y=2\hfill \\ 5x+3y=5\hfill \end{array}$

$\{\begin{array}{c}-x+3y=8\hfill \\ 2x-6y=\mathrm{-20}\hfill \end{array}$

The sum of two numbers is $\mathrm{-90}$ . Their difference is $16$ . Find the numbers.

Omar stops at a donut shop every day on his way to work. Last week he had 8 donuts and 5 cappuccinos, which gave him a total of 3,000 calories. This week he had 6 donuts and 3 cappuccinos, which was a total of 2,160 calories. How many calories are in one donut? How many calories are in one cappuccino?