방정식과 부등식 전체 문제

In the following exercise, evaluate each determinant by expanding by minors along the first row.

$|\begin{array}{ccccccc}-2 & & & -3 & & & -4 \\ 5 & & & -6 & & & 7 \\ -1 & & & 2 & & & 0\end{array}|$

In the following exercise, evaluate each determinant by expanding by minors.

$|\begin{array}{ccccccc}3 & & & 5 & & & 4 \\ -1 & & & 3 & & & 0 \\ -2 & & & 6 & & & 1\end{array}|$

Use Cramer’s Rule to Solve Systems of Equations

In the following exercises, solve each system of equations using Cramer’s rule

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

Use Cramer’s Rule to Solve Systems of Equations

In the following exercises, solve each system of equations using Cramer’s rule

$\left\{\begin{array}{l}4x-3y+z=7 \\ 2x-5y-4z=3 \\ 3x-2y-2z=-7\end{array}\right.$

Use Cramer’s Rule to Solve Systems of Equations

In the following exercises, solve each system of equations using Cramer’s rule

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

Use Cramer’s Rule to Solve Systems of Equations

In the following exercises, solve each system of equations using Cramer’s rule

$\left\{\begin{array}{l}x+y-3z=-1 \\ y-z=0 \\ -x+2y=1\end{array}\right.$

Use Cramer’s Rule to Solve Systems of Equations

In the following exercises, solve each system of equations using Cramer’s rule

$\left\{\begin{array}{l}3x+4y-3z=-2 \\ 2x+3y-z=-12 \\ x+y-2z=6\end{array}\right.$

Solve Applications Using Determinants

In the following exercises, determine whether the given points are collinear.

$(0,2),$ $(-1,-1),$ and $(-2,4)$

Determine Whether an Ordered Pair is a Solution of a System of Linear Inequalities

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

$\left\{\begin{array}{l}4x+y>6 \\ 3x-y\le 12\end{array}\right.$

ⓐ $(2,-1)$ ⓑ $(3,-2)$

Determine Whether an Ordered Pair is a Solution of a System of Linear Inequalities

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

$\left\{\begin{array}{l}y>\frac{1}{3}x+2 \\ x-\frac{1}{4}y\le 10\end{array}\right.$

ⓐ $(6,5)$ ⓑ $(15,8)$

Solve a System of Linear Inequalities by Graphing

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}y\le 3x+2 \\ y>-x-1\end{array}\right.$

Solve a System of Linear Inequalities by Graphing

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}x-y>-1 \\ y<\frac{1}{3}x-2\end{array}\right.$

Solve a System of Linear Inequalities by Graphing

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}2x-3y<6 \\ 3x+4y\ge 12\end{array}\right.$

Solve a System of Linear Inequalities by Graphing

In the following exercises, solve each system by graphing.

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

Solve a System of Linear Inequalities by Graphing

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}x+3y<5 \\ y\ge -\frac{1}{3}x+6\end{array}\right.$

Solve a System of Linear Inequalities by Graphing

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}y\ge 2x-5 \\ -6x+3y>-4\end{array}\right.$

Roxana makes bracelets and necklaces and sells them at the farmers’ market. She sells the bracelets for $12 each and the necklaces for $18 each. At the market next weekend she will have room to display no more than 40 pieces, and she needs to sell at least $500 worth in order to earn a profit.

ⓐ Write a system of inequalities to model this situation.

ⓑ Graph the system.

ⓒ Should she display 26 bracelets and 14 necklaces?

ⓓ Should she display 39 bracelets and 1 necklace?

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.

ⓐ Write a system of inequalities to model this situation.

ⓑ Graph the system.

ⓒ Can she buy 8 paperback books and 40 hardcover books?

ⓓ Can she buy 10 paperback books and 37 hardcover books?

In the following exercises, solve the following systems by graphing.

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

In the following exercises, solve the following systems by graphing.

$\left\{\begin{array}{l}x-y>-2 \\ y\le 3x+1\end{array}\right.$