Chapter 8

In Exercises \(1-6\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{array}{l} y \geq 3 x-3 \\ y \leq-x+1 \end{array}\right. $$

The total cost of 15 gallons of regular gasoline and 10 gallons of premium gasoline is \(\$ 97.15\). Premium gasoline costs \(\$ 0.24\) more per gallon than regular gasoline. What is the cost per gallon of each type of gasoline? (a) Write a verbal model for this problem. (b) Assign labels to the verbal model. (c) Use the labels to write a linear system. (d) Solve the system and answer the question.

In Exercises \(1-6\), solve the system by the method of elimination. $$ \left\\{\begin{array}{l} x-y=4 \\ x+y=12 \end{array}\right. $$

In Exercises 1-4, solve the system by the method of substitution. $$ \left\\{\begin{array}{l} y=2 x-1 \\ y=-x+5 \end{array}\right. $$

In Exercises \(1-4\), determine whether each ordered pair is a solution of the system. \(\left\\{\begin{array}{r}x+3 y=11 \\ -x+3 y=7\end{array}\right.\) (a) \((2,3)\) (b) \((5,4)\)

In Exercises \(1-6\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{array}{l} y \geq 2 x-3 \\ y \leq 3 x+1 \end{array}\right. $$

A total of \(\$ 12,000\) is invested in two bonds that pay \(10.5 \%\) and \(12 \%\) simple interest. (There is more risk in the \(12 \%\) bond.) The combined annual interest is \(\$ 1380\). How much is invested in each bond? (a) Write a verbal model for this problem. (b) Assign labels to the verbal model. (c) Use the labels to write a linear system. (d) Solve the system and answer the question.

In Exercises \(1-6\), solve the system by the method of elimination. $$ \left\\{\begin{array}{l} x+y=7 \\ x-y=3 \end{array}\right. $$

In Exercises 1-4, solve the system by the method of substitution. $$ \left\\{\begin{array}{l} y=-2 x+9 \\ y=3 x-1 \end{array}\right. $$

In Exercises \(1-4\), determine whether each ordered pair is a solution of the system. $$ \left\\{\begin{aligned} 3 x-y &=-2 \\ x-3 y &=2 \end{aligned}\right. $$ (a) \((0,2)\) (b) \((-1,-1)\)

In Exercises \(1-6\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{aligned} x+2 y &>-4 \\ y &

A bakery with two stores buys three large delivery trucks and six small delivery trucks. One store receives one large delivery truck and four small delivery trucks for a total cost of \(\$ 118,000\). The second store receives two large delivery trucks and two small delivery trucks for a total cost of \(\$ 107,000\). What is the cost of each type of delivery truck?

In Exercises \(1-6\), solve the system by the method of elimination. $$ \left\\{\begin{array}{r} -x+2 y=12 \\ x+6 y=20 \end{array}\right. $$

In Exercises 1-4, solve the system by the method of substitution. $$ \left\\{\begin{array}{r} x-y=0 \\ 2 x+y=9 \end{array}\right. $$

In Exercises \(1-4\), determine whether each ordered pair is a solution of the system. $$ \left\\{\begin{array}{r} 2 x-3 y=-8 \\ x+y=1 \end{array}\right. $$ (a) \((5,-3)\) (b) \((-1,2)\)

In Exercises \(1-6\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{aligned} x+y &<-3 \\ y &>3 x-4 \end{aligned}\right. $$

A furniture company with two stores buys three large delivery trucks and four small delivery trucks. One store receives one large delivery truck and three small delivery trucks for a total cost of \(\$ 157,000\). The second store receives two large delivery trucks and one small delivery truck for a total cost of \(\$ 139,000\). What is the cost of each type of delivery truck?

In Exercises \(1-6\), solve the system by the method of elimination. $$ \left\\{\begin{array}{l} x+2 y=14 \\ x-2 y=10 \end{array}\right. $$

In Exercises 1-4, solve the system by the method of substitution. $$ \left\\{\begin{array}{r} x-y=0 \\ 5 x-3 y=10 \end{array}\right. $$

In Exercises \(1-4\), determine whether each ordered pair is a solution of the system. $$ \left\\{\begin{aligned} 5 x-3 y &=-12 \\ x-4 y &=1 \end{aligned}\right. $$ (a) \((-3,-1)\) (b) \((3,1)\)

In Exercises \(1-6\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{array}{l} x+y \leq 3 \\ x-y \leq 1 \end{array}\right. $$

How many liters of a \(35 \%\) alcohol solution and a \(60 \%\) alcohol solution must be mixed to obtain 10 liters of a \(50 \%\) alcohol solution?

In Exercises \(1-6\), solve the system by the method of elimination. $$ \left\\{\begin{array}{l} 3 x-5 y=1 \\ 2 x+5 y=9 \end{array}\right. $$

In Exercises 5-14, solve the system by the method of substitution. $$ \left\\{\begin{array}{l} x=4 y-5 \\ x=3 y \end{array}\right. $$

In Exercises \(5-10\), solve the system by graphing. $$ \left\\{\begin{array}{l} y=-x+3 \\ y=x+1 \end{array}\right. $$

In Exercises \(1-6\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{array}{l} x+y \geq 2 \\ x-y \leq 2 \end{array}\right. $$

Ten gallons of a \(30 \%\) acid solution is obtained by mixing a \(20 \%\) acid solution with a \(50 \%\) acid solution. How many gallons of each solution must be used to obtain the desired mixture?

In Exercises \(1-6\), solve the system by the method of elimination. $$ \left\\{\begin{aligned} -2 x+3 y &=-4 \\ 2 x-4 y &=6 \end{aligned}\right. $$

In Exercises 5-14, solve the system by the method of substitution. $$ \left\\{\begin{array}{l} x=-5 y-2 \\ x=2 y-23 \end{array}\right. $$

In Exercises \(5-10\), solve the system by graphing. $$ \left\\{\begin{array}{l} y=2 x-1 \\ y=x+1 \end{array}\right. $$

In Exercises \(7-16\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{array}{l} x<3 \\ x>-2 \end{array}\right. $$

In Exercises \(7-10\), use a system of linear equations to solve the problem. The selling price of a watch is \(\$ 108.75\). The markup rate is \(45 \%\) of the wholesale cost. Find the wholesale cost.

In Exercises 7-12, solve the system by the method of elimination. $$ \left\\{\begin{array}{l} 2 a+5 b=3 \\ 2 a+b=9 \end{array}\right. $$

In Exercises 5-14, solve the system by the method of substitution. $$ \left\\{\begin{array}{r} 2 x=8 \\ x-2 y=12 \end{array}\right. $$

In Exercises \(5-10\), solve the system by graphing. $$ \left\\{\begin{array}{l} y=2 x-4 \\ y=-\frac{1}{2} x+1 \end{array}\right. $$

In Exercises \(7-16\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{array}{l} y>-1 \\ y \leq 2 \end{array}\right. $$

In Exercises \(7-10\), use a system of linear equations to solve the problem. The selling price of a cellular phone is \(\$ 149.92\). The markup rate is \(60 \%\) of the wholesale cost. Find the wholesale cost.

In Exercises 7-12, solve the system by the method of elimination. $$ \left\\{\begin{array}{r} 4 a+5 b=9 \\ 2 a+5 b=7 \end{array}\right. $$

In Exercises 5-14, solve the system by the method of substitution. $$ \left\\{\begin{array}{r} 2 x-y=0 \\ 3 y=6 \end{array}\right. $$

In Exercises \(5-10\), solve the system by graphing. $$ \left\\{\begin{array}{l} y=\frac{1}{2} x+2 \\ y=-x+8 \end{array}\right. $$

In Exercises \(7-16\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{array}{l} y

In Exercises \(7-10\), use a system of linear equations to solve the problem. The sale price of a microwave oven is \(\$ 110\). The discount is \(20 \%\) of the original price. Find the original price.

In Exercises 7-12, solve the system by the method of elimination. $$ \left\\{\begin{array}{r} -x+2 y=6 \\ 2 x+5 y=6 \end{array}\right. $$

In Exercises 5-14, solve the system by the method of substitution. $$ \left\\{\begin{aligned} x-2 y &=-10 \\ 3 x-y &=0 \end{aligned}\right. $$

In Exercises \(5-10\), solve the system by graphing. $$ \left\\{\begin{array}{l} x-y=3 \\ x+y=3 \end{array}\right. $$

In Exercises \(7-16\), sketch the graph of the system of linear inequalities. $$ \left\\{\begin{array}{l} y>x-4 \\ x>-1 \end{array}\right. $$

In Exercises \(7-10\), use a system of linear equations to solve the problem. The sale price of a treadmill is \(\$ 280\). The discount is \(30 \%\) of the original price. Find the original price.

In Exercises 7-12, solve the system by the method of elimination. $$ \left\\{\begin{array}{r} -4 x+8 y=0 \\ 3 x-2 y=2 \end{array}\right. $$

In Exercises 5-14, solve the system by the method of substitution. $$ \left\\{\begin{array}{r} x-2 y=5 \\ 3 x-y=0 \end{array}\right. $$

In Exercises \(5-10\), solve the system by graphing. $$ \left\\{\begin{array}{l} x-y=0 \\ x+y=4 \end{array}\right. $$