Exam 4: Systems of Equations and Inequalities

Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest. $\left[ \begin{array} { c c c } 6 & 8 & - 5 \\- 7 & 3 & 8 \\- 8 & - 2 & 5\end{array} \right]$

Graph the system of linear inequalities below. $\left\{ \begin{array} { l } 4 x + 3 y \leq 8 \\x - y \leq 2\end{array} \right.$

Graph the system of linear inequalities below. $\left\{ \begin{array} { l } y \geq \frac { 1 } { 2 } x - 2 \\y \leq 2 x - 2\end{array} \right.$

Laws that deal with electrical currents are known as Kirchhoff s Laws. When Kirchhoff s Laws are applied to the electrical network shown in the figure, where $R _ { 1 } = 4$ ohms, $R _ { 2 } = 2$ ohms, $R _ { 3 } = 4$ ohms, $V _ { 1 } = 26$ volts, $V _ { 2 } = 14$ volts, the currents $I _ { 1 } , I _ { 2 }$ and $I _ { 3 }$ (in amps)are the solution of the system $\left\{ \begin{array} { l } I _ { 1 } + I _ { 2 } - I _ { 3 } = 0 \\4 I _ { 1 } + 2 I _ { 3 } = 26 \\4 I _ { 1 } - 4 I _ { 2 } = 12\end{array} \right.$ Find the current $I _ { 3 }$ .

Use matrices to solve the system of linear equations below. $\left\{ \begin{array} { r } 4 x - 2 y - 3 z = 1 \\x - z = - 1 \\5 x - 3 y - 4 z = 2\end{array} \right.$

Use matrices to solve the system of linear equations below. $\left\{ \begin{array} { r } x - 2 z = 7 \\4 x - 4 y - z = 9 \\x - 2 y - 3 z = 20\end{array} \right.$

Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest. $\left[ \begin{array} { c c c } - 1 & 0 & - 1 \\0 & 1 & 0 \\1 & 2 & - 2\end{array} \right]$

A coffee manufacturer sells a 18 -pound package of coffee that consists of three flavors of coffee. Vanilla flavored coffee costs $2.25 per pound, Hazelnut flavored coffee costs $2.5 per pound, and French Roast flavored coffee costs $3 per pound. The package contains the same amount of Hazelnut coffee as French Roast coffee. The cost of the 18 -pound package is $46.5 . How many pounds of $\text { Vanilla }$ flavored coffee are there in the package?

Solve the system of linear equations below by the method of elimination, if a single solution exists. $\left\{ \begin{array} { c } - 2 x + y = 7 \\2 x - 5 y = - 27\end{array} \right.$

Graph the equations below and determine the solution if it exists. $\left\{ \begin{array} { l } 4.5 x + 4 y = 20.5 \\13.5 x + 12 y = 61.5\end{array} \right.$

Graph the equations below and determine the solution if it exists. $\left\{ \begin{array} { l } - 2 x - y = 2 \\10 x + 5 y = 30\end{array} \right.$

Use matrices to solve the system of linear equations below. $\left\{ \begin{array} { l } 2 x - y = - 3 \\x - 2 y = 6\end{array} \right.$

You receive a total of 1,350 a year in interest from three investments. The interest rates for the three investments are $5 \% , 6.5 \%$ and 7.5% . The 6.5% investment is half of the 5% investment, and the 7.5% investment is 3000 less than the 5% investment. What is the amount of the $6.5 \%$ investment?

Match the system of linear inequalities below with its graph. $\left\{ \begin{array} { l } y \geq - 2 \\y < 1\end{array} \right.$

Use matrices to solve the system of linear equations below. $\left\{ \begin{array} { l } 3 x + 3 y = 18 \\2 x + 3 y = 13 \\4 x + z = 24\end{array} \right.$

A corporation borrowed $\$ 1,330,000$ to expand its line of clothing. Some of the money was borrowed at $8 \%$ some at $11 \%$ and the remainder at $14 \%$ . The annual interest payment to the lenders was $\$ 127,400$ . The amount borrowed at $8 \%$ was $4$ times the amount borrowed at $14 \%$ . How much was borrowed at the $14 \%$ rate?

Determine which of the following ordered pairs, $( 3 , - 7 )$ , $( 8,4 )$ , $( 8 , - 3 )$ , $( - 6 , - 7 )$ , or $( 9 , - 8 )$ is a solution to the system of equations below. $\left\{ \begin{array} { l } 6 x - 9 y = 81 \\- 2 x - y = 1\end{array} \right.$

Solve the system of linear equations below by the method of elimination. $\left\{ \begin{array} { c } x + y = - 6 \\- x + 2 y = - 3\end{array} \right.$

Determine the order of the given matrix below. $\left[ \begin{array} { c c c } - 4 & 4 & 0 \\2 & - 5 & 5 \\- 5 & 0 & - 3\end{array} \right]$

Solve the system of linear equations below. $\left\{ \begin{array} { r } x - 3 y + 4 z = 13 \\3 x - 2 z = - 8 \\2 x - 5 y - z = - 9\end{array} \right.$