방정식과 부등식 전체 문제

Solve a System of Equations by Substitution

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

$\left\{\begin{array}{l}y=-\frac{1}{3}x+2 \\ x+3y=6\end{array}\right.$

Solve a System of Equations by Elimination

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

$\left\{\begin{array}{l}x+y=12 \\ x-y=-10\end{array}\right.$

Solve a System of Equations by Elimination

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

$\left\{\begin{array}{l}3x-8y=20 \\ x+3y=1\end{array}\right.$

Solve a System of Equations by Elimination

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

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

Solve a System of Equations by Elimination

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

$\left\{\begin{array}{l}\frac{1}{3}x-\frac{1}{2}y=1 \\ \frac{3}{4}x-y=\frac{5}{2}\end{array}\right.$

Solve a System of Equations by Elimination

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

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

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.

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

Mollie wants to plant 200 bulbs in her garden, all 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.

The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle. Find the measure of both angles.

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?

Jack has $12,000 to invest and wants to earn 7.5% interest per year. He will put some of the money into a savings account that earns 4% per year and the rest into CD account that earns 9% per year. How much money should he put into each account?

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 $1,585. What is the amount of each loan?

Solve Systems of Equations with Three Variables

In the following exercises, determine whether the ordered triple is a solution to the system.

$\left\{\begin{array}{l}3x-4y-3z=2 \\ 2x-6y+z=3 \\ 2x+3y-2z=3\end{array}\right.$ ⓐ $(2,3,-1)$ ⓑ $(3,1,3)$

Solve Systems of Equations with Three Variables

In the following exercises, determine whether the ordered triple is a solution to the system.

$\left\{\begin{array}{l}y=\frac{2}{3}x-2 \\ x+3y-z=15 \\ x-3y+z=-2\end{array}\right.$ ⓐ $\left(-6,5,\frac{1}{2}\right)$ ⓑ $\left(5,\frac{4}{3},-3\right)$

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

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

Solve a System of Linear Equations with Three Variables

In the following exercises, solve the system of equations.

$\left\{\begin{array}{l}x+\frac{5}{2}y+z=-2 \\ 2x+2y+\frac{1}{2}z=-4 \\ \frac{1}{3}x-y-z=1\end{array}\right.$