Review Exercises

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

ⓐ $\left(6,2\right)$ ⓑ $\left(9,\mathrm{-1}\right)$

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

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

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

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

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

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?

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

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

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

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

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?

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

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

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

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?

$\{\begin{array}{c}y=3x-9\hfill \\ 4x-5y=23\hfill \end{array}$

Four times a number plus three times a second number is $\mathrm{-9}$. Twice the first number plus the second number is three. Find the numbers.

Henri has $24,000 invested in stocks and bonds. The amount in stocks is $6,000 more than three times the amount in bonds. How much is each investment?

Mollie wants to plant 200 bulbs in her garden. She wantsall irises and tulips. She wants to plant three times as many tulips as irises. How many irises and how many tulips should she plant?

Two angles are complementary. The measure of the larger angle is five more than four times the measure of the smaller angle. Find the measures of both angles.

The perimeter of a city rectangular park is 1428 feet. The length is 78 feet more than twice the width. Find the length and width of the park.

Bob left home, riding his bike at a rate of 10 miles per hour to go to the lake. Cheryl, his wife, left 45 minutes $(\frac{3}{4}$ hour) later, driving her car at a rate of 25 miles per hour. How long will it take Cheryl to catch up to Bob?

A passenger jet can fly 804 miles in 2 hours with a tailwind but only 776 miles in 2 hours into a headwind. Find the speed of the jet in still air and the speed of the wind.

Priam has dimes and pennies in a cup holder in his car. The total value of the coins is $4.21. The number of dimes is three less than four times the number of pennies. How many dimes and how many pennies are in the cup?

A scientist needs 70 liters of a 40% solution of alcohol. He has a 30% and a 60% solution available. How many liters of the 30% and how many liters of the 60% solutions should he mix to make the 40% solution?

When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was $1585. What is the amount of each loan?

$\{\begin{array}{c}y>\frac{1}{3}x+2\hfill \\ x-\frac{1}{4}y\le 10\hfill \end{array}$

ⓐ $(6,5)$ ⓑ $(15,8)$

$\{\begin{array}{c}x-y>\mathrm{-1}\hfill \\ y<\frac{1}{3}x-2\hfill \end{array}$

$\{\begin{array}{c}y\le -\frac{3}{4}x+1\hfill \\ x\ge \mathrm{-5}\hfill \end{array}$

$\{\begin{array}{c}y\ge 2x-5\hfill \\ \mathrm{-6}x+3y>\mathrm{-4}\hfill \end{array}$

Annie has a budget of $600 to purchase paperback books and hardcover books for her classroom. She wants the number of hardcover to be at least 5 more than three times the number of paperback books. Paperback books cost $4 each and hardcover books cost $15 each.

1. ⓐ Write a system of inequalities to model this situation.
2. ⓑ Graph the system.
3. ⓒ Can she buy 8 paperback books and 40 hardcover books?
4. ⓓ Can she buy 10 paperback books and 37 hardcover books?