91Ó°ÊÓ

Solve the systems of equations. Three oil pumps fill three different tanks. The pumping rates of the pumps (in \(L / h\) ) are \(r_{1}, r_{2},\) and \(r_{3},\) respectively. Because of malfunctions, they do not operate at capacity each time. Their rates can be found by solving the following system of equations: $$\begin{aligned}r_{1}+r_{2}+r_{3} &=14,000 \\\r_{1}+2 r_{2} &=13,000 \\\3 r_{1}+3 r_{2}+2 r_{3} &=36,000\end{aligned}$$

Solve the given systems of equations by use of determinants. (Exercises \(17-26\) are the same as Exercises \(3-12\) of Section \(5.6 .)\) $$\begin{aligned} &3 r+s-t=2\\\ &r+t-2 s=0\\\ &4 r-s+t=3 \end{aligned}$$

Solve the given systems of equations by the method of elimination by addition or subtraction. $$\begin{aligned} &3 x-y=5\\\ &3 y-9 x=-15 \end{aligned}$$

Solve the given systems of equations by determinants. (These are the same as those for Exercises \(15-24\) of Section \(5.4 .\) ) $$\begin{aligned} &R-4 r=17\\\ &4 r+3 R=3 \end{aligned}$$

Solve each system of equations to the nearest 0.001 for each variable by using a calculator. $$\begin{aligned} &1.2 x-2.4 y=4.8\\\ &3.0 x=-2.0 y+7.2 \end{aligned}$$

Find the slope and the \(y\) -intercept of the line with the given equation and sketch the graph using the slope and the \(y\) -intercept. A calculator can be used to check your graph. $$y=-4 x$$

Solve the given systems of equations by determinants. (These are the same as those for Exercises \(15-24\) of Section \(5.4 .\) ) $$\begin{aligned} &12 t+9 y=14\\\ &6 t=7 y-16 \end{aligned}$$

Find the slope and the \(y\) -intercept of the line with the given equation and sketch the graph using the slope and the \(y\) -intercept. A calculator can be used to check your graph. $$y=x-4$$

Solve each system of equations to the nearest 0.001 for each variable by using a calculator. $$\begin{aligned} &4.0 x-3.5 y=1.5\\\ &1.4 y+0.2 x=1.4 \end{aligned}$$

Solve the given systems of equations by the method of elimination by addition or subtraction. $$\begin{aligned} &2 x-3 y-4=0\\\ &3 x+2=2 y \end{aligned}$$