91Ó°ÊÓ

Solve the given systems of equations by using an appropriate algebraic method. $$\begin{aligned} &3 R=8-5 I\\\ &6 I=8 R+11 \end{aligned}$$

Sketch the line with the given slope and \(y\) -intercept. $$m=\frac{1}{2},(0,0)$$

Solve the given systems of equations by either method of this section. $$\begin{aligned} &15 x+10 y=11\\\ &20 x-25 y=7 \end{aligned}$$

Solve each system of equations to the nearest 0.001 for each variable by using a calculator. $$\begin{aligned} &x=4 y+2\\\ &3 y=2 x+3 \end{aligned}$$

Solve the given systems of equations by determinants. All numbers are approximate. \(0.3 x-0.7 y=0.4\) \(0.2 x+0.5 y=0.7\)

Solve the systems of equations. In Exercises \(25-32\) it is necessary to set up the appropriate equations. All numbers are accurate to at least three significant digits. A university graduate school conferred 420 advanced academic degrees at graduation. There were 100 more \(\mathrm{MA}\) degrees than \(\mathrm{MS}\) and PhD degrees combined, and 3 times as many MS degrees as PhD degrees. How many of each were awarded?

Solve the given systems of equations by using an appropriate algebraic method. $$\begin{aligned} &90 x-110 y=40\\\ &30 x-15 y=25 \end{aligned}$$

Solve the given systems of equations by determinants. All numbers are approximate. \(250 R+225 Z=400\) \(375 R-675 Z=325\)

Solve the given systems of equations by using an appropriate algebraic method. $$\begin{aligned} &0.42 x-0.56 y=1.26\\\ &0.98 x-1.40 y=-0.28 \end{aligned}$$

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