Exam 3: Systems of Linear Equations

Determine whether the system is inconsistent, dependent, or neither. - $\left\{ \begin{array} { l } 3 x + y - 3 z = - 2 \\- x - 3 y + 2 z = - 3 \\- 4 x - 4 y + 5 z = - 1\end{array} \right.$

Solve the system by the addition method. - $\left\{ \begin{array} { l } 6 x + 3 y = 51 \\2 x - 6 y = 38\end{array} \right.$

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use the information in the figure to answer the question. -What is the profit when 878 binoculars are produced?

Determine whether the given ordered pair is a solution to the system. - $\left\{ \begin{array} { l } ( 6 , - 2 ) \\3 x + y = 16 \\2 x + 3 y = 6\end{array} \right.$

Solve the problem. -A twin-engined aircraft can fly 672 miles from city A to city B in 3 hours with the wind and make the return trip in 7 hours against the wind. What is the speed of the wind?

Solve the problem. -Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 9 times as many dimes as nickels, and the value of the dimes is $3.40 more than the value of the nickels. How many nickels and dimes does Jamil have?

Solve the system. If there is no solution or if the system's equations are dependent, so state. - $\left\{ \begin{array} { r } x + 9 y - z = 4 \\5 x + 45 y - 5 z = 20 \\3 x + 27 y - 3 z = 12\end{array} \right.$

Solve the system by any method. - $\left\{ \begin{array} { l } 9 x = 22 - 8 y \\- 4 x + 3 y = 23\end{array} \right.$

Solve the system by any method. - $\left\{ \begin{array} { l } 3 x - 9 y = 7 \\- 6 x + 18 y = - 28\end{array} \right.$

Solve the system by graphing. -

Solve the problem. -Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the dollar amount coming in and going out at the break-even point. Round to the nearest dollar if necessary. C(x)=76x+3080 R(x)=104x

Solve the system by graphing. - $\left\{ \begin{array} { l } 5 x + y = - 20 \\2 x + 4 y = 10\end{array} \right.$

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { l } ( - 2,5 , - 3 ) \\x - y + z = 6 \\x + y + z = 0 \\x + y - z = 4\end{array} \right.$

Solve the system by the substitution method. - $\left\{ \begin{array} { l } 5 x + 3 y = 80 \\2 x + y = 30\end{array} \right.$

Solve the problem. -A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $6.00. Another customer buys 5 hot dogs and 4 bags of potato chips for $13.75. Find the cost of each item.

Solve the system by the addition method. - $\left\{ \begin{array} { r } 8 x - 7 y = 6 \\- 32 x + 28 y = - 18\end{array} \right.$

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { l } ( 2,3,1 ) \\ 4 x + 4 y + z = 18 \\ 5 x + 5 y - z = - 12\end{array} \right.$

Determine whether the given ordered pair is a solution to the system. - (-6,2) x+y=8 x-y=4

Solve the system by any method. - $\left\{ \begin{array} { l } 7 x - 3 y = 8 \\28 x - 12 y = 16\end{array} \right.$

Determine whether the given ordered pair is a solution to the system. - (-6,2) x+y=-4 x-y=-8