Chapter 4

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}-3 x+y=-1 \\\x-2 y=4\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}y \geq 2 x+1 \\\y \leq 4\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{aligned} x+2 y &=-1 \\ 4 x-5 y &=22 \end{aligned}\right.$$

A restaurant purchased eight tablecloths and five napkins for 106 dollar A week later, a tablecloth and six napkins were bought for 24 dollar Find the cost of one tablecloth and the cost of one napkin, assuming the same prices for both purchases.

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}x+y=2 \\\x-y=4\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}-4 x+y=-11 \\\2 x-3 y=5\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}y \geq \frac{1}{2} x+2 \\\y \leq 2\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{rr} -3 x+7 y= & 14 \\ 2 x-y= & -13 \end{array}\right.$$

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}x+y=1 \\ y-x=3\end{array}\right.$$

The perimeter of a badminton court is 128 feet. After a game of badminton, a player's coach estimates that the athlete has run a total of 444 feet, which is equivalent to six times the court's length plus nine times its width. What are the dimensions of a standard badminton court?

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}x=9-2 y \\\x+2 y=13\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}y>x-1 \\\x>5\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 2 x-5 y=-1 \\ 3 x+y=7 \end{array}\right.$$

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}x+y=4 \\ y-x=4\end{array}\right.$$

The perimeter of a tennis court is 228 feet. After a round of tennis, a player's coach estimates that the athlete has run a total of 690 feet, which is equivalent to 7 times the court's length plus four times its width. What are the dimensions of a standard tennis court?

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}6 x+2 y=7 \\\y=2-3 x\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}y>x-2 \\\x>3\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 3 x-14 y=6 \\ 5 x+7 y=10 \end{array}\right.$$

A rectangular lot whose perimeter is 320 feet is fenced along three sides. An expensive fencing along the lot's length costs 16 dollar per foot. An inexpensive fencing along the two side widths costs only 5 dollar per foot. The total cost of the fencing along the three sides comes to 2140 dollar What are the lot's dimensions?

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}2 x-3 y=6 \\ 4 x+3 y=12\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}y \geq 2 x-3 \\\y \leq 2 x+1\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=3 x-5 \\\21 x-35=7 y\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 5 x-4 y=19 \\ 3 x+2 y=7 \end{array}\right.$$

A rectangular lot whose perimeter is 1600 feet is fenced along three sides. An expensive fencing along the lot's length costs 20 dollar per foot. An inexpensive fencing along the two side widths costs only 5 dollar per foot. The total cost of the fencing along the three sides comes to 13,000 dollar What are the lot's dimensions?

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}x+2 y=2 \\ x-y=2\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}y \geq 3 x-2 \\\y \leq 3 x+1\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}9 x-3 y=12 \\\y=3 x-4\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 3 x-4 y=11 \\ 2 x+3 y=-4 \end{array}\right.$$

You are choosing between two telephone plans. Plan A has a monthly fee of 20 dollar with a charge of 0.05 dollar per minute for all calls. Plan B has a monthly fee of 5 dollar with a charge of 0.10 dollar per minute for all calls. a. For how many minutes of calls will the costs for the two plans be the same? What will be the cost for each plan? b. If you make approximately 10 calls per month, each averaging 20 minutes, which plan should you select? Explain your answer.

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}4 x+y=4 \\ 3 x-y=3\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}5 x+2 y=0 \\\x-3 y=0\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}y>2 x-3 \\\y \leq-x+6\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 2 x+3 y=-16 \\ 5 x-10 y=30 \end{array}\right.$$

You are choosing between two telephone plans. Plan A has a monthly fee of 15 dollar with a charge of 0.08 dollar per minute for all calls. Plan B has a monthly fee of 3 dollar with a charge of 0.12 dollar per minute for all calls. a. For how many minutes of calls will the costs for the two plans be the same? What will be the cost for each plan? b. If you make approximately 15 calls per month, each averaging 30 minutes, which plan should you select? Explain your answer.

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}5 x-y=10 \\ 2 x+y=4\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}4 x+3 y=0 \\\2 x-y=0\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}y<-2 x+4 \\\y \leq x-4\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{rr} 3 x+2 y= & -1 \\ -2 x+7 y= & 9 \end{array}\right.$$

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of 100 dollar and you pay \(80 \%\) of the manufacturer's recommended list price. Plan B offers an annual membership fee of 40 dollar and you pay \(90 \%\) of the manufacturer's recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=x+5 \\ y=-x+3\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}2 x-y=6 \\\3 x+2 y=5\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x+2 y \leq 4 \\\y \geq x-3\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 5 x+3 y=27 \\ 7 x-2 y=13 \end{array}\right.$$

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of 300 dollar and you pay \(70 \%\) of the manufacturer's recommended list price. Plan B offers an annual membership fee of 40 dollar and you pay \(90 \%\) of the manufacturer's recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost for each plan?

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=x+1 \\ y=3 x-1\end{array}\right.$$

Solve each system by the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}2 x-y=4 \\\3 x-5 y=2\end{array}\right.$$

Graph the solution set of each system of linear inequalities. $$\left\\{\begin{array}{l}x+y \leq 4 \\\y \geq 2 x-4\end{array}\right.$$

In Exercises \(1-44,\) solve each system by the addition method. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l} 3 x=2 y+7 \\ 5 x=2 y+13 \end{array}\right.$$

A community center sells a total of 301 tickets for a basketball game. An adult ticket costs 3 dollar A student ticket costs 1 dollar The sponsors collect 487 dollar in ticket sales. Find the number of each type of ticket sold.

Solve each system by graphing. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. $$\left\\{\begin{array}{l}y=2 x \\ y=-x+6\end{array}\right.$$