Exam 3: Systems of Linear Equations

Solve the problem. -Andrea is having her yard landscaped. She obtained an estimate from two landscaping companies. Company A gave an estimate of $190 for materials and equipment rental plus $50 per hour for labor. Company B gave an estimate of $260 for materials and equipment rental plus $40 per hour for labor. Create a cost equation for each company where y is the total cost of the landscaping and x is the number of hours of labor. Determine how many hours of labor will be required for the two companies to cost the same.

Solve the system by the substitution method. - $\left\{ \begin{array} { l } 2 x + y = 10 \\2 x + y = 18\end{array} \right.$

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. -Is there a profit when 966 binoculars are produced?

Solve the problem. -Find the values of $a , b$ , and $c$ such that the graph of the quadratic equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 1,10 ) , ( 2,1 )$ , and $( 4 , - 15 )$ .

Solve the system by the substitution method. - $\left\{ \begin{array} { l } x + y = - 7 \\x - y = 15\end{array} \right.$

Solve the system by graphing. - $\left\{ \begin{array} { l } 3 x + 3 y = 33 \\2 x + 3 y = 28\end{array} \right.$

Solve the system by the addition method. - $\left\{ \begin{array} { l } 6 x + 27 y = 27 \\5 x - 9 y = - 9\end{array} \right.$

Solve the system. If there is no solution or if the system's equations are dependent, so state. - $\left\{ \begin{array} { r r } 7 x - 8 y + 9 z = & - 7 \\8 x + 4 y + 7 z = & 8 \\28 x - 32 y + 36 z = & 8\end{array} \right.$

Solve the system by the substitution method. - $\left\{ \begin{array} { l } 3 x + y = 11 \\9 x + 3 y = 33\end{array} \right.$

Solve the system by any method. - $\left\{ \begin{array} { r } 3 x + y = 2 \\- 12 x - 4 y = - 8\end{array} \right.$

Determine if the given ordered triple is a solution of the system. - $\left\{ \begin{array} { c } ( 3 , - 2,0 ) \\2 x - y + 5 z = 17 \\x + 5 y + z = 3\end{array} \right.$

Solve the system. If there is no solution or if the system's equations are dependent, so state. - $\left\{ \begin{array} { r r } x - y + 2 z = & - 2 \\4 x + z = & 0 \\- x + y - 2 z = & 6\end{array} \right.$

Solve the system by the substitution method. - $\left\{ \begin{aligned}x & = - 4 y + 4 \\7 x - 5 y & = - 5\end{aligned} \right.$

Solve the system by the substitution method. - $\left\{ \begin{array} { r r } 9 x + y = & 0 \\- 9 x + y = & - 18\end{array} \right.$

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. -Is there a profit when 676 binoculars are produced?

Solve the problem. -A college student earned $8400 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 8%. If the student received a total of $720 in interest at the end of the year, how much was invested at 10%?

Solve the problem. -The graph shows the results of an ongoing survey of 500 random students at State University from 2007 through 2012. The survey asked whether students bought the majority of their music on CD or if they downloaded the majority of their music as MP3 files from the internet. Use the graph to estimate the point of intersection. In what year was the number of students who bought the majority of their music on CDs and the number of students who downloaded the majority of their music as MP3 files the same? How many students were there for each?

Solve the problem. -An electronics company kept comparative statistics on two products, A and B. For the years 2003 to 2011, the total number of Product A ever sold (in thousands) is given by the equation y = 74x + 250, where x is the number of years since 2003. For that same period, the total number of Product B ever sold (in thousands) is given by the equation y = -30x + 434, where x is the number of years since 2003. Use the substitution method to solve the system and choose the statement that most accurately describes the solution.

Determine whether the given ordered pair is a solution to the system. - (-1,3) 3x+y=-6 4x+3y=-13

Solve the problem. -Given the cost function, $C ( x )$ , and the revenue function, $R ( x )$ , find the number of units $x$ that must be sold to brea C(x)=7000x+63,000 R(x)=14,000x