Chapter 5

Solve each system by substitution. $$\begin{aligned}&\frac{2}{3} x+\frac{2}{3} y=6\\\&\frac{3}{2} x-\frac{1}{4} y=\frac{13}{2}\end{aligned}$$

Write a system of equations and solve. Sally invested \(\$ 4000\) in two accounts, some of it at \(3 \%\) simple interest, the rest in an account earning \(5 \%\) simple interest. How much did she invest in each account if she earned \(\$ 144\) in interest after one year?

Solve each system using the elimination method. $$\begin{aligned}0.1 x+2 y &=-0.8 \\\0.03 x+0.10 y &=0.26\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&\frac{x}{10}-\frac{y}{2}=\frac{13}{10}\\\&\frac{1}{3} x+\frac{5}{4} y=-\frac{3}{2}\end{aligned}$$

Write a system of equations and solve. Diego inherited \(\$ 20,000\) and puts some of it into an account earning \(4 \%\) simple interest and the rest in an account earning \(7 \%\) simple interest. He earns a total of \(\$ 1130\) in interest after a year. How much did he deposit into each account?

\(\begin{aligned} x-\frac{5}{2} y+\frac{1}{2} z &=\frac{5}{4} \\ x+3 y-z &=4 \\\\-6 x+15 y-3 z &=-1 \end{aligned}\)

Graph the line containing the given point and with the given slope. $$(-3,-2) ; m=4$$

Solve each system using the elimination method. $$\begin{array}{c}0.6 x-0.1 y=0.5 \\\0.10 x-0.03 y=-0.01\end{array}$$

Solve each system by substitution. $$\begin{aligned}&\frac{4}{9} x-\frac{5}{3} y=-\frac{1}{9}\\\&\frac{x}{5}+\frac{y}{5}=-1\end{aligned}$$

Write a system of equations and solve. Josh saves all of his quarters and dimes in a bank. When he opens it, he has 110 coins worth a total of S18.80. How many quarters and how many dimes does he have?

Solve each system \(\begin{aligned} a+b+9 c &=-3 \\\\-5 a-2 b+3 c &=10 \\ 4 a+3 b+6 c &=-15 \end{aligned}\)

Graph the line containing the given point and with the given slope. $$(1,5) ; m=-3$$

Solve each system using the elimination method. $$\begin{aligned}&0.02 x+0.07 y=-0.24\\\&0.05 y-0.04 x=0.10\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&\frac{3}{4} x+\frac{5}{2} y=5\\\&\frac{3}{2} x-\frac{1}{6} y=-\frac{1}{3}\end{aligned}$$

Write a system of equations and solve. Mrs. Kowalski bought nine packages of batteries when they were on sale. The AA batteries cost \(\$ 1.00\) per package and the \(C\) batteries cost \(\$ 1.50\) per package. If she spent \(\$ 11.50,\) how many packages of each type of battery did she buy?

Solve each system \(\begin{aligned} 2 x+3 y &=2 \\\\-3 x+4 z &=0 \\ y-5 z &=-17 \end{aligned}\)

Graph the line containing the given point and with the given slope. $$(-2,6) ; m=-\frac{5}{2}$$

Solve each system using the elimination method. $$\begin{aligned}0.8 x-0.3 y &=0.5 \\\0.07 x+0.05 y &=0.12\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&\frac{1}{6} x+\frac{4}{3} y=\frac{13}{3}\\\&\frac{2}{5} x+\frac{3}{2} y=\frac{18}{5}\end{aligned}$$

Write a system of equations and solve. How much pure acid and how many liters of a \(10 \%\) acid solution should be mixed to get \(12 \mathrm{L}\) of a \(40 \%\) acid solution?

Solve each system \(\begin{aligned} 2 x-y+4 z &=-1 \\ x+3 y+z &=-5 \\\\-3 x+2 y &=7 \end{aligned}\)

Solve each system using the elimination method. $$\begin{aligned}&2(y-6)=3 y+4(x-5)\\\&2(4 x+3)-5=2(1-y)+5 x\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&\frac{5}{3} x-\frac{4}{3} y=-\frac{4}{3}\\\&y=2 x+4\end{aligned}$$

Write a system of equations and solve. How many ounces of pure orange jurce and how many ounces of a citrus fruit drink containing \(5 \%\) fruit juice should be mixed to get 76 oz of a fruit drink that is \(25 \%\) fruit juice?

Solve each system \(a+3 b-8 c=2\) \(-2 a-5 b+4 c=-1\) \(4 a+b+16 c=-4\)

Graph the line containing the given point and with the given slope. $$(5,2) ; m=0$$

Solve each system using the elimination method. $$\begin{aligned}&5(2 x+3)-3 x=6(x+2)+4 y\\\&3(4 y-1)-x=2(x-4)+7 y\end{aligned}$$

Solve each system by substitution. $$\begin{aligned}&\frac{3}{4} x+\frac{1}{2} y=6\\\&x=3 y+8\end{aligned}$$

Write a system of equations and solve. Moe buys two bot does, two orders of frics, and a large soda for \(\mathbf{S} 9.00 .\) Larry buys two hot dogs, cone order of fries, and two large sodas for \(\$ 9.50,\) and Curly spends S11.00 on three hot dogs, two orders of fries, and a large soda. Find the price of a bot dog. an order of fries, and a large soda.

Write a system of equations and solve. A car and a truck leave the same location, the car headed east and the truck headed west. The truck's speed is 10 mph less than the speed of the car. After \(3 \mathrm{hr}\), the car and truck are \(330 \mathrm{mi}\) apart. Find the speed of each vehicle.

Identify the slope and \(y\) -intercept, then graph the line. $$y=x-3$$

Solve each system using the elimination method. $$\begin{aligned}&20+3(2 y-3)=4(2 y-1)-9 x\\\&5(3 x-4)+8 y=3 x+7(y-1)\end{aligned}$$

Solve each system by substitution. $$\begin{array}{c}0.2 x-0.1 y=0.1 \\\0.01 x+0.04 y=0.23\end{array}$$

Write a system of equations and solve. A movie theater charges \(\$ 9.00\) for an adult's ticket. S7. OO for a ticket for scriors 60 and over, and \(\$ 6,00\) for a child's ticket. For a particular movie, the theater sold a total of 290 tickets. which brought in \(\$ 2400\). The number of semors' 'tickets sold was twice the number of children's tickets sold. Determine the number of ndults", scniors', and children's tickets sold.

Write a system of equations and solve. A passenger train and a freight train leave cities 400 mi apart and travel toward each other. The passenger train is traveling 20 mph faster than the freight train. Find the speed of each train if they pass each other after 5 hr.

Identify the slope and \(y\) -intercept, then graph the line. $$y=-2 x+7$$

Solve each system using the elimination method. $$\begin{aligned}&6(3 x+4)-8(x+2)=5-3 y\\\&6 x-2(5 y+2)=-7(2 y-1)-4\end{aligned}$$

Solve each system by substitution. $$\begin{array}{l}0.01 x+0.10 y=-0.11 \\\0.02 x-0.01 y=0.20\end{array}$$

Write a system of equations and solve. Olivia can walk \(8 \mathrm{mi}\) in the same amount of time she can bike 22 mi. She bikes 7 mph faster than she walks. Find her walking and biking speeds.

Identify the slope and \(y\) -intercept, then graph the line. $$y=-\frac{3}{4} x+1$$

Solve each system using the elimination method. $$\begin{aligned}&6(x-3)+x-4 y=1+2(x-9)\\\&4(2 y-3)+10 x=5(x+1)-4\end{aligned}$$

Solve each system by substitution. $$\begin{array}{r}0.1 x+0.5 y=0.4 \\\\-0.03 x+0.01 y=0.2\end{array}$$

Write a system of equations and solve. A small, private plane can fly \(400 \mathrm{mi}\) in the same amount of time a jet can fly 1000 mi. If the jet's speed is 300 mph more than the speed of the small plane, find the speeds of both planes. (THE IMAGES CANNOT COPY)

Identify the slope and \(y\) -intercept, then graph the line. $$y=\frac{1}{4} x-2$$

Solve each system using the elimination method. $$\begin{aligned}&12 x-4(2 y+3)=5(x-y)\\\&18-5(2 x+5)=-3(x+4)-y+1\end{aligned}$$

Solve each system by substitution. $$\begin{array}{c}-0.02 x+0.05 y=0.4 \\\0.01 x-0.03 y=-0.25\end{array}$$

The three NBA teams with the highest revenues in \(2002-2003\) were the New York Knicks, the Los Angeles Lakers, and the Chicago Bulls. Their revenues totalled \(\$ 428\) million. The Lakers took in \(\$ 30\) million more than the Bulls, and the Knicks took in \(\$ 11\) million more than the Lakers. Determine the revenue of each team during the \(2002-2003\) season. (Source. Forbes Feb. \(16,2004, p .66\)

Write a system of equations and solve. Nick and Scott leave opposite ends of a bike trail \(13 \mathrm{mi}\) apart and travel toward each other. Scott is traveling 2 mph slower than Nick. Find each of their speeds if they meet after 30 min.

Identify the slope and \(y\) -intercept, then graph the line. $$x-3 y=-6$$

Solve each system using the elimination method twice. $$\begin{aligned}&4 x+5 y=-6\\\&3 x+8 y=15\end{aligned}$$