방정식과 부등식 전체 문제

Solve a System of Equations by Elimination

In the following exercises, solve the systems of equations by elimination.

$\left\{\begin{array}{l}9x+4y=2 \\ 5x+3y=5\end{array}\right.$

Solve a System of Equations by Elimination

In the following exercises, solve the systems of equations by elimination.

$\left\{\begin{array}{l}-x+3y=8 \\ 2x-6y=-20\end{array}\right.$

The sum of two numbers is $-90$. 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?

Choose the Most Convenient Method to Solve a System of Linear Equations

In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination.

$\left\{\begin{array}{l}6x-5y=27 \\ 3x+10y=-24\end{array}\right.$

Choose the Most Convenient Method to Solve a System of Linear Equations

In the following exercises, decide whether it would be more convenient to solve the system of equations by substitution or elimination.

$\left\{\begin{array}{l}y=3x-9 \\ 4x-5y=23\end{array}\right.$

The sum of two numbers is $-32$. One number is two less than twice the other. Find the numbers.

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

Last month Jim and Debbie earned $7,200. Debbie earned $1,600 more than Jim earned. How much did they each earn?

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?

Pam is 3 years older than her sister, Jan. The sum of their ages is 99. Find their ages.

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?

The difference of two supplementary angles is 58 degrees. Find the measures of the angles.

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.

Becca is hanging a 28 foot floral garland on the two sides and top of a pergola to prepare for a wedding. The height is four feet less than the width. Find the height and width of the pergola.

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.

Sheila and Lenore were driving to their grandmother’s house. Lenore left one hour after Sheila. Sheila drove at a rate of 45 mph, and Lenore drove at a rate of 60 mph. How long will it take for Lenore to catch up to Sheila?

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?

Marcus can drive his boat 36 miles down the river in three hours but takes four hours to return upstream. Find the rate of the boat in still water and the rate of the current.

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.