Chapter 9

Unknowns in the Denominator $$\begin{aligned} &\frac{5}{3 a}+\frac{2}{5 b}=7\\\ &\frac{7}{6 a}-3=\frac{1}{10 b} \end{aligned}$$

Solve for \(x, y,\) and \(z\). \(x-y=a\) \(y+z=3 a\) \(5 z-x=2 a\)

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{array}{l} 7 x-4 y=81 \\ 5 x-3 y=57 \end{array}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{array}{l} 3 x+4 y=85 \\ 5 x+4 y=107 \end{array}$$

Unknowns in the Denominator $$\begin{aligned} &\frac{8.10}{5.10 t}+\frac{1.40}{3.60 s}=1.80\\\ &\frac{2.10}{1.40 s}-\frac{1.30}{5.20 t}+3.10=0 \end{aligned}$$

Solve for \(x, y,\) and \(z\). \(a x+b y=(a+b) c\) \(b y+c z=(c+a) b\) \(a x+c z=(b+c) a\)

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &3 x-2 y=1\\\ &2 x+y=10 \end{aligned}$$

Solve for \(x\) and \(y\) in terms of the other literal quantities. $$\begin{aligned} &a x+2 b y=1\\\ &3 a x+b y=2 \end{aligned}$$

Solve for \(x, y,\) and \(z\). \(x+y+2 z=2(b+c)\) \(x+2 y+z=2(a+c)\) \(2 x+y+z=2(a+b)\)

Applications to Work, Fluid Flow, and Energy Flow Working together, two conveyors can fill a certain bin in \(6.00 \mathrm{h}\). If one conveyor works 1.80 times as fast as the other, how long would it take each to fill the bin working alone?

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

Solve for \(x\) and \(y\) in terms of the other literal quantities. $$\begin{aligned} &m x+3 n y=2\\\ &2 m x+n y=1 \end{aligned}$$

When writing Kirchhoff's voltage law for a certain three-loop network, we get the set of equations $$\begin{aligned}3 I_{1}+2 I_{2}-4 I_{3} &=4 \\\I_{1}-3 I_{2}+2 I_{3} &=-5 \\\2 I_{1}+I_{2}-I_{3} &=3\end{aligned}$$ where \(I_{1}, I_{2},\) and \(I_{3}\) are the loop currents in amperes. Solve for these currents.

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &y=9-3 x\\\ &x=8-2 y \end{aligned}$$

Solve for \(x\) and \(y\) in terms of the other literal quantities. $$\begin{aligned} &2 p x+3 q y=3\\\ &3 p x+2 q y=4 \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &y=2 x-3\\\ &x=19-3 y \end{aligned}$$

Solve for \(x\) and \(y\) in terms of the other literal quantities. $$\begin{array}{l} 7 c x+3 d y=5 \\ 2 c x+8 d y=6 \end{array}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &2 x+3 y=9\\\ &5 x+4 y=5 \end{aligned}$$

Solve for \(x\) and \(y\) in terms of the other literal quantities. $$\begin{aligned} &3 x-2 y=a\\\ &2 x+y=b \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &x-2 y=11\\\ &y=5 x-10 \end{aligned}$$

Solve for \(x\) and \(y\) in terms of the other literal quantities. $$\begin{aligned} &a x+b y=r\\\ &a x+c y=s \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &29.1 x-47.6 y=42.8\\\ &11.5 x+72.7 y=25.8 \end{aligned}$$

Solve for \(x\) and \(y\) in terms of the other literal quantities. $$\begin{aligned} &a x-d y=c\\\ &m x-n y=c \end{aligned}$$

Project: Solve the following set of equations. This will give us formulas for solving a set of three equations, which we will find useful in the next chapter. $$\begin{array}{l} a_{1} x+b_{1} y+c_{1} z=k_{1} \\ a_{2} x+b_{2} y+c_{2} z=k_{2} \\ a_{3} x+b_{3} y+c_{3} z=k_{3} \end{array} $$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &4.92 x-8.27 y=2.58\\\ &6.93 x+2.84 y=8.36 \end{aligned}$$

Solve for \(x\) and \(y\) in terms of the other literal quantities. $$\begin{aligned} &p x-q y+p q=0\\\ &2 p x-3 q y=0 \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &4 n=18-3 m\\\ &m=8-2 n \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &5 p+4 q-14=0\\\ &17 p=31+3 q \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{array}{l} 3 w=13+5 z \\ 4 w-7 z-17=0 \end{array}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &3 u=5+2 v\\\ &5 v+2 u=16 \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &3.62 x=11.7+4.73 y\\\ &4.95 x-7.15 y-12.8=0 \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &3.03 a=5.16+2.11 b\\\ &5.63 b+2.26 a=18.8 \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &4.17 w=14.7-3.72 v\\\ &v=8.11-2.73 w \end{aligned}$$

Solve each system of equations by addition-subtraction, or by substitution. Check some by graphing. $$\begin{aligned} &5.66 p+4.17 q-16.9=0\\\ &13.7 p=32.2+3.61 q \end{aligned}$$