Exam 42: Two Variable Linear Systems

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $\left\{ \begin{array} { l } 3 x + 2 y = 10 \\2 x + 5 y = 3\end{array} \right.$ ​

Use any method to solve the system of linear equations,find (x,y).​ $\left\{ \begin{array} { l } y = 4 x - 7 \\y = 7 x - 13\end{array} \right.$ ​

A total of $23,000 is invested in two corporate bonds that pay 3.5% and 5% simple interest.The investor wants an annual interest income of $880 from the investments.What amount should be invested in the 3.5% bond? ​

Find the equilibrium point (x,p)of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. ​ Demand Supply $p = 150 - 0.07 x$ $p = 65 + 0.1 x$ ​

Use any method to solve the system of linear equations,find (x,y).​ $\left\{ \begin{array} { c } 4 x - 5 y = 13 \\5 x + y = 9\end{array} \right.$ ​

One eight-ounce glass of apple juice and one eight-ounce glass of orange juice contain a total of 176.4 milligrams of vitamin C.Twoeight-ounce glasses of apple juice and three eight-ounce glasses of orange juice contain a total of 432.7 milligrams of vitamin C.How much vitamin C is in an eight-ounce glass of each type of juice? ​

Solve the system of linear equations by the method of elimination.Use the graph to check your solution.​ $\left\{ \begin{array} { c } x - y = 2 \\- 2 x + 2 y = 9\end{array} \right.$ ​

Solve the system of linear equations by the method of elimination.Use the graph to check your solution.​ $\left\{ \begin{array} { l } 9 x + 4 y = 4 \\18 x + 8 y = 16\end{array} \right.$ ​​

​Solve the system of linear equations by the method of elimination,find (x,y).​ $\left\{ \begin{array} { c } - 5 x + 2 y = - 38 \\3 x - y = 23\end{array} \right.$ ​ ​

Find the equilibrium point (x,p)of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. ​ Demand Supply $p = 140 - 0.00003 x$ $p = 90 + 0.00001 x$ ​

Solve the system of linear equations by the method of elimination,find (x,y). ​​ $\left\{ \begin{array} { l } \frac { x + 23 } { 8 } + \frac { y + 10 } { 7 } = 3 \\x - 9 y = 20\end{array} \right.$ ​

​Seven hundred gallons of 89-octane gasoline is obtained by mixing 87-octane gasoline with 92-octane gasoline.How much of each type of gasoline is required to obtain the 700 gallons of 89-octane gasoline? Use this system of linear equations there x and y represent the number of gallons of the 87-octane gasoline and 89-octane gasoline. ​​ $\left\{ \begin{array} { c } x + y = 700 \\87 x + 92 y = 62300\end{array} \right.$ ​

Solve the system of linear equations by the method of elimination.Find (r,s)and check your solution algebraically.​ $\left\{ \begin{array} { c } 2 r + 4 s = 7 \\16 r + 50 s = 77\end{array} \right.$ ​

Solve the system of linear equations by the method of elimination.Use the graph to check your solution.​ $\left\{ \begin{array} { l } 2 x + y = 2 \\x - y = 4\end{array} \right.$ ​​

Fourty liters of a 40% acid solution is obtained by mixing a 28% solution with a 50% solution.Write a system of equations in which one equation represents the amount of final mixture required and the other represents the percent of acid in the final mixture.Let x and y represent the amounts of the 28% and 50% solutions,respectively. ​

Find the equilibrium point (x,p)of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. ​ Demand Supply $p = 570 - 0.5 x$ $p = 370 + 0.3 x$ ​

​Use any method to solve the system of linear equations,find (x,y).​ $\left\{ \begin{array} { l } x - 3 y = 25 \\4 x + 3 y = 25\end{array} \right.$ ​

Use any method to solve the system of linear equations,find (x,y). ​​ $\left\{ \begin{array} { l } y = - 7 x - 12 \\y = 7 - 8 x\end{array} \right.$ ​

Find the equilibrium point (x,p)of the demand and supply equations.The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations. ​ Demand Supply $p = 410 - 0.0004 x$ $p = 230 + 0.0002 x$ ​

Solve the system of linear equations by the method of elimination.Find (x,y)and check your solution algebraically.​ $\left\{ \begin{array} { l } 2 x + 7 y = \frac { 112 } { 9 } \\\\7 x + 8 y = \frac { 62 } { 9 }\end{array} \right.$ ​