Exam 42: Two Variable Linear Systems

​Solve the system of linear equations by the method of elimination,find (x,y). ​​ $\left\{ \begin{array} { l } - 0.06 x + 0.01 y = 0.03 \\- 0.09 x - 0.04 y = 0.09\end{array} \right.$ ​

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $\left\{ \begin{array} { l } 3 x + 11 y = 12 \\- 2 x - 5 y = 6\end{array} \right.$ ​

Thirty​ liters of a 40% acid solution is obtained by mixing a 28% solution with a 43% solution.How much of each solution is required to obtain the specified concentration of the final mixture? Use this system of linear equations there x and y represents the amounts of the 28% solution and 43% solution. ​​ $\left\{ \begin{array} { l } x + y = 30 \\0.28 x + 0.43 y = 12\end{array} \right.$ ​

​Solve the system of linear equations using any method,find (x,y). ​​ $\left\{ \begin{array} { r } 9 x - 2 y = 1 \\- 3 x + 2 y = 7\end{array} \right.$ ​

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $\left\{ \begin{array} { c } 5 x + 3 y = 6 \\3 x - y = 5\end{array} \right.$ ​

An airplane flying into a headwind travels 1128.00 miles in 4 hours and 42 minutes.On the return flight,the distance is traveled in 4 hours.Find the airspeed of the plane and the speed of the wind,assuming that both remain constant. ​

A total of $32,000 is invested in two municipal bonds that pay 5.75% and 6.25% simple interest.The investor wants an annual interest income of $1,900 from the investments.What amount should be invested in the 5.75% bond? ​

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. ​​ $\left\{ \begin{array} { c } x + y = 0 \\9 x + 8 y = 1\end{array} \right.$ ​​

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically. ​​ $\left\{ \begin{array} { c } 5 x + 7 y = 21 \\- 14 x - 18 y = - 38\end{array} \right.$ ​

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. ​​ $\left\{ \begin{array} { c } 5 x - y = - 5 \\10 x + 3 y = - 10\end{array} \right.$ ​

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $\left\{ \begin{array} { l } x + 2 y = 6 \\x - 2 y = 2\end{array} \right.$ ​

Sixty liters of a 43% acid solution is obtained by mixing a 28% solution with a 42% solution.Use a graphing utility to graph the two given equations.Let x and y represent the amounts of the 28 % solution and 42% solution.As the amount of the 28% solution increases,how does the amount of the 42% solution change? $\left\{ \begin{array} { l } x + y = 60 \\0.28 x + 0.42 y = 25.8\end{array} \right.$ ​ ​ ​

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $\left\{ \begin{array} { l } 4 b + 4 m = \frac { 156 } { 35 } \\\\4 b + 11 m = \frac { 471 } { 35 }\end{array} \right.$ ​

Two cheeseburgers and one small order of French fries from a fast-food restaurant contain a total of 850 calories.Three cheeseburgers and two small orders of French fries contain a total of 1380 calories.Find the caloric content of each item. ​

Seven hundred gallons of 87-octane gasoline is obtained by mixing 87-octane gasoline with 90-octane gasoline.Use a graphing utility to graph the two given equations.Let x and y represent the number of gallons of the 87-octane gasoline and 90-octane gasoline.As the number of gallons of the 87-octane gasoline increases,how does the number of gallons of the 90-octane gasoline change?​ $\left\{ \begin{array} { l } x + y = 700 \\87 x + 90 y = 60,900\end{array} \right.$ ​

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $\left\{ \begin{array} { r } x + 5 y = 11 \\3 x - 10 y = 18\end{array} \right.$ ​

​Solve the system of linear equations using any method,find (x,y). ​​ $\left\{ \begin{array} { l } 3 x + 8 y = 2 \\y = x - 5\end{array} \right.$ ​

Use any method to solve the system of linear equations,find (x,y). ​​ $\left\{ \begin{array} { c } 4 x - 3 y = 16 \\- 5 x + 3 y = - 23\end{array} \right.$ ​

​Solve the system of linear equations by the method of elimination,find (x,y). ​​ $\left\{ \begin{array} { c } \frac { 9 } { 4 } x + \frac { 1 } { 4 } y = \frac { - 7 } { 4 } \\9 x + y = - 7\end{array} \right.$ ​

Solve the system of linear equations by the method of elimination.Find (u,v)and check your solution algebraically.​ $\left\{ \begin{array} { l } 5 u + 6 v = 28 \\3 u + 5 v = 20\end{array} \right.$ ​