Chapter 9

Solve each systems of equations by any method. $$\begin{array}{l} x+y=35 \\\x+z=40 \\\y+z=45\end{array}$$

Applications. To determine the speed of a boat, it is clocked, with the current, to go a distance of 18.5 miles in 1.31 hours. Returning the same distance against the current took 3.32 h. Find (a) the speed of the boat in still water and (b) the speed of the current.

Solve simultaneously. Check some by calculator. $$\begin{aligned} &\frac{x}{5}+\frac{y}{6}=18\\\ &\frac{x}{2}-\frac{y}{4}=21 \end{aligned}$$

Graphically find the approximate solution to each system of equations. If you have a graphics calculator, use the \([\mathrm{ZOOM}]\) and \(\mathrm{TRACE}\). or \([\text { INTERSECT }]\) features to find the solution. $$\begin{aligned} &2 x-y=5\\\ &x-3 y=5 \end{aligned}$$

Solve each systems of equations by any method. $$\begin{aligned} &x+y+z=12\\\ &x-y=2\\\ &x-z=4 \end{aligned}$$

Applications. A certain river has a speed of \(2.50 \mathrm{mi} / \mathrm{h} .\) A rower travels downstream for \(1.50 \mathrm{h}\) and returns in \(4.50 \mathrm{h} .\) Find his rate in still water, and find the one-way distance traveled.

Solve simultaneously. Check some by calculator. $$\begin{aligned} &\frac{x}{2}+\frac{y}{3}=7\\\ &\frac{x}{3}+\frac{y}{4}=5 \end{aligned}$$

Graphically find the approximate solution to each system of equations. If you have a graphics calculator, use the \([\mathrm{ZOOM}]\) and \(\mathrm{TRACE}\). or \([\text { INTERSECT }]\) features to find the solution. $$\begin{aligned} x+2 y &=-7 \\ 5 x-y &=9 \end{aligned}$$

Solve each systems of equations by any method. $$\begin{aligned} &3 x+y=5\\\ &2 y-3 z=-5\\\ &x+2 z=7 \end{aligned}$$

Solve simultaneously. Check some by calculator. $$\begin{aligned} &\frac{x}{3}+\frac{y}{4}=8\\\ &x-y=-3 \end{aligned}$$

Graphically find the approximate solution to each system of equations. If you have a graphics calculator, use the \([\mathrm{ZOOM}]\) and \(\mathrm{TRACE}\). or \([\text { INTERSECT }]\) features to find the solution. $$\begin{aligned} &x-2 y=-3\\\ &3 x+y=5 \end{aligned}$$

Solve each systems of equations by any method. $$\begin{aligned} &x-y=5\\\ &y-z=-6\\\ &2 x-z=2 \end{aligned}$$

Solve simultaneously. Check some by calculator. $$\begin{aligned} &\frac{x}{2}+\frac{y}{3}=5\\\ &\frac{x}{3}+\frac{y}{2}=5 \end{aligned}$$

Graphically find the approximate solution to each system of equations. If you have a graphics calculator, use the \([\mathrm{ZOOM}]\) and \(\mathrm{TRACE}\). or \([\text { INTERSECT }]\) features to find the solution. $$\begin{aligned} &4 x+y=8\\\ &2 x-y=7 \end{aligned}$$

Solve each systems of equations by any method. $$\begin{array}{l} x+y+z=18 \\ x-y+z=6 \\ x+y-z=4 \end{array}$$

Applications. A certain investment, at simple interest, amounted in 5 years to \(\$ 3000\) and in 6 years to \(\$ 3100 .\) Find the amount invested, to the nearest dollar, and the rate of interest. Use the simple interest formula, \(y=a(1+n t)\)

Solve simultaneously. Check some by calculator. $$\begin{aligned} &\frac{3 x}{5}+\frac{2 y}{3}=17\\\ &\frac{2 x}{3}+\frac{3 y}{4}=19 \end{aligned}$$

Graphically find the approximate solution to each system of equations. If you have a graphics calculator, use the \([\mathrm{ZOOM}]\) and \(\mathrm{TRACE}\). or \([\text { INTERSECT }]\) features to find the solution. $$\begin{aligned} &2 x+5 y=4\\\ &5 x-2 y=-3 \end{aligned}$$

Solve each systems of equations by any method. $$\begin{aligned} &x+y+z=90\\\ &2 x-3 y=-20\\\ &2 x+3 z=145 \end{aligned}$$

Applications. A shipment of 21 computer keyboards and 33 monitors cost \(\$ 35,564.25 .\) Another shipment of 41 keyboards 36 monitors cost \(\$ 49,172.50 .\) Find the cost of each keyboard and each monitor.

Solve simultaneously. Check some by calculator. $$\begin{aligned} &\frac{x}{7}+7 y=251\\\ &\frac{y}{7}+7 x=299 \end{aligned}$$

Solve each systems of equations by any method. \(x+2 y+3 z=14\) \(2 x+y+2 z=10\) \(3 x+4 y-3 z=2\)

Solve simultaneously. Check some by calculator. $$\begin{aligned} &\frac{m}{2}+\frac{n}{3}-3=0\\\ &\frac{n}{2}+\frac{m}{5}=\frac{23}{10} \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &2 x+y=11\\\ &3 x-y=4 \end{aligned}$$

Solve each systems of equations by any method. \(x+y+z=35\) \(x-2 y+3 z=15\) \(y-x+z=-5\)

Solve simultaneously. Check some by calculator. $$\begin{aligned} &\frac{p}{6}-\frac{q}{3}+\frac{1}{3}=0\\\ &\frac{2 p}{3}-\frac{3 q}{4}-1=0 \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &x-y=7\\\ &3 x+y=5 \end{aligned}$$

Solve each systems of equations by any method. \(x-2 y+2 z=5\) \(5 x+3 y+6 z=57\) \(x+2 y+2 z=21\)

Solve simultaneously. Check some by calculator. $$\begin{array}{l} \frac{r}{6.20}-\frac{s}{4.30}=\frac{1}{3.10} \\\ \frac{r}{4.60}-\frac{s}{2.30}=\frac{1}{3.50} \end{array}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &4 x+2 y=3\\\ &-4 x+y=6 \end{aligned}$$

Solve each systems of equations by any method. \(1.21 x+1.48 y+1.63 z=6.83\) \(4.94 x+4.27 y+3.63 z=21.7\) \(2.88 x+4.15 y-2.79 z=2.76\)

Unknowns in the Denominator $$\begin{aligned} &\frac{8}{x}+\frac{6}{y}=3\\\ &\frac{6}{x}+\frac{15}{y}=4 \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &2 x-3 y=5\\\ &3 x+3 y=10 \end{aligned}$$

Solve each systems of equations by any method. \(5 a+b-4 c=-5\) \(3 a-5 b-6 c=-20\) \(a-3 b+8 c=-27\)

Unknowns in the Denominator $$\begin{aligned} &\frac{1}{x}+\frac{3}{y}=11\\\ &\frac{5}{x}+\frac{4}{y}=22 \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &3 x-2 y=-15\\\ &5 x+6 y=3 \end{aligned}$$

Solve each systems of equations by any method. \(p+3 q-r=10\) \(5 p-2 q+2 r=6\) \(3 p+2 q+r=13\)

Applications Involving Mixtures. A distributor has two gasohol blends: one that contains \(5.00 \%\) alcohol and another with \(11.0 \%\) alcohol. How many gallons of each must be mixed to make 500 gal of gasohol containing \(9.50 \%\) alcohol?

Unknowns in the Denominator $$\begin{aligned} &\frac{5}{x}+\frac{6}{y}=7\\\ &\frac{7}{x}+\frac{9}{y}=10 \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &7 x+6 y=20\\\ &2 x+5 y=9 \end{aligned}$$

Fractional Equations. \(x+\frac{y}{3}=5\) \(x+\frac{z}{3}=6\) \(y+\frac{z}{3}=9\)

Unknowns in the Denominator $$\begin{aligned} &\frac{2}{x}+\frac{4}{y}=14\\\ &\frac{6}{x}-\frac{2}{y}=14 \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &x+5 y=11\\\ &3 x+2 y=7 \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &4 x-5 y=-34\\\ &2 x-3 y=-22 \end{aligned}$$

Unknowns in the Denominator $$\begin{aligned} &\frac{6}{x}+\frac{8}{y}=1\\\ &\frac{7}{x}-\frac{11}{y}=-9 \end{aligned}$$

Fractional Equations. \(\frac{x}{10}+\frac{y}{5}+\frac{z}{20}=\frac{1}{4}\) \(x+y+z=6\) \(\frac{x}{3}+\frac{y}{2}+\frac{z}{6}=1\)

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &x=11-4 y\\\ &5 x-2 y=11 \end{aligned}$$

Unknowns in the Denominator $$\begin{aligned} &\frac{2}{5 x}+\frac{5}{6 y}=14\\\ &\frac{2}{5 x}-\frac{3}{4 y}=-5 \end{aligned}$$

Fractional Equations. \(\frac{1}{x}+\frac{2}{y}-\frac{1}{z}=-3\) \(\frac{3}{x}+\frac{1}{y}+\frac{1}{z}=4\) \(\frac{1}{x}-\frac{1}{y}+\frac{2}{z}=6\)

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &2 x-3 y=3\\\ &4 x+5 y=39 \end{aligned}$$