91Ó°ÊÓ

Decide whether the given ordered pair is a solution of the given system. $$ \begin{aligned} &\begin{array}{c} {(2,-3)} \\ {x+y=-1} \end{array}\\\ &2 x+5 y=19 \end{aligned} $$

Solve each system by the elimination method. Check each solution. See Examples I and 2. $$ \begin{aligned} 2 x+y &=-5 \\ x-y &=2 \end{aligned} $$

Solve each system by the substitution method. Check each solution. $$ \begin{aligned} &\frac{x}{2}+\frac{y}{3}=\frac{7}{6}\\\ &\frac{x}{4}-\frac{3 y}{2}=\frac{9}{4} \end{aligned} $$

Write a system of equations for each problem, and then solve the system. A \(90 \%\) antifreeze solution is to be mixed with a \(75 \%\) solution to make \(120 \mathrm{L}\) of a \(78 \%\) solution. How many liters of the \(90 \%\) and \(75 \%\) solutions will be used? $$ \begin{array}{|c|c|c|} \hline \text { Liters of } & {\text { Percent (as }} & {\text { Liters of }} \\\ {\text { Solution }} & {\text { a decimal )}} & {\text { Pure Antifreeze }} \\\ {x} & {0.90} \\ {y} & {0.75} \\ {120} & {0.78} & {} \\ \hline \end{array} $$

Without graphing, answer the following questions for each linear system. (a) Is the system inconsistent, are the equations dependent, or neither? (b) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line? (c) Does the system have one solution, no solution, or an infinite number of solutions? $$ \begin{aligned} &y-x=-5\\\ &x+y=1 \end{aligned} $$

Write a system of equations for each problem, and then solve the system. RAGBRAI", the Des Moines Register's Annual Great Bicycle Ride Across Iowa, is the longest and oldest touring bicycle ride in the world. Suppose a cyclist began the \(471 \mathrm{mi}\) ride on July \(20,2008,\) in western Iowa at the same time that a car traveling toward it left eastern Iowa. If the bicycle and the car met after 7.5 hr and the car traveled \(35.8 \mathrm{mph}\) faster than the bicycle, find the average rate of each.

Without graphing, answer the following questions for each linear system. (a) Is the system inconsistent, are the equations dependent, or neither? (b) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line? (c) Does the system have one solution, no solution, or an infinite number of solutions? $$ \begin{aligned} &2 x-y=4\\\ &y+4=2 x \end{aligned} $$

Without graphing, answer the following questions for each linear system. (a) Is the system inconsistent, are the equations dependent, or neither? (b) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line? (c) Does the system have one solution, no solution, or an infinite number of solutions? $$ \begin{aligned} &2 x+3 y=12\\\ &2 x-y=4 \end{aligned} $$

Solve each system by the elimination method. $$ \begin{aligned} &24 x+12 y=-7\\\ &16 x-18 y=17 \end{aligned} $$

Simplify. $$ (-6 x+8 y)+(6 x+2 y) $$