Exam 4: Systems of Equations and Inequalities

Solve the problem. -On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $4 each and a number of necklaces at $9 each. She wrote a check for $980 to pay for the order. How many bracelets and How many necklaces did Rosaria purchase?

Solve the system. - $\left\{ \begin{aligned}x + y & = - 7 \\2 x - 2 y + 3 z & = 13 \\x - z & = - 9\end{aligned} \right.$

Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even. - C(x)=11x+15,200 R(x)=30x

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { l } 2 x + y = 8 \\6 x + 3 y = 24\end{array} \right.$

Solve the system of linear equations using matrices. - $\left\{ \begin{aligned}4 x - y + 8 z & = 50 \\- 6 x + 4 z & = - 36 \\4 y + z & = 27\end{aligned} \right.$

Write the word or phrase that best completes each statement or answers the question. The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost and revenue equations. -For what x-values will the company make a profit?

Write the word or phrase that best completes each statement or answers the question. The revenue equation for a certain brand of mouthwash is y = 1.3x, where x is the number of bottles of mouthwash sold and y is the total income for selling x bottles. The cost equation is y = 0.5x + 2500, where x is the number of bottles of mouthwash manufactured and y is the cost of producing x bottles. The following set of axes shows the graph of the cost and revenue equations. -For what x-values will the company lose money?

Solve the system of equations. - $\left\{ \begin{aligned}y & = - 3 x \\- 3 x + y & = - 6\end{aligned} \right.$

Determine whether the ordered pair is a solution of the system of linear equations $( 4,3 ) , \left\{ \begin{array} { l } 4 x + y = 13 \\3 x + 4 y = 0\end{array} \right.$

Solve the system. - $\left\{ \begin{array} { r r } x - 5 y - z = & 5 \\- 3 x + 15 y + 3 z = & - 15 \\4 x - 20 y - 4 z = & 20\end{array} \right.$

Solve the system of linear equations using matrices. - $\left\{ \begin{array} { r } x + 5 y + 5 z = 33 \\4 y + 2 z = 22 \\2 z = 2\end{array} \right.$