Exam 3: Systems of Linear Equations and Inequalities

Use the matrix features on a graphing calculator to express the augmented matrix in reduced row echelon form. $\left[ \begin{array} { c c | c } 1 & 5 & 13 \\3 & - 2 & 5\end{array} \right]$

Solve the system by using the Gauss-Jordan method. x+5y =-3 -3x-15y =9

Identify the inequalities that match the given graph.

The Walnut Cove Ruritan Club sells hot dogs and drinks from a concession stand at the annual 4th of July parade. Carl bought 6 hot dogs and 4 drinks and paid $17.00. Susan purchased 3 hot dogs And 4 drinks and was charged $12.50. What is the cost of 1 hot dog and what is the cost of 1 drink?

A triangle has one angle that measures 5° more than 2 times the smallest angle, and the largest angle measures 65° less than 3 times the measure of the smallest angle. Find the measures of the three Angles.

Graph the solution set of the compound inequality. $2 y + 4 x \geq 4$ and $y \geq 5$

Paula invested into two accounts; one pays 7% simple interest and the other pays 8% simple interest. She invested $2000 more in the account paying 8% than in the account paying 7%. At the End of the first year, Paula's total return was $1810. How much did she invest in each account?

Which is not a solution of $10 > x - 7 y$ ?

Solve the system. y =-x-2 x+5y =3

Given the matrix R $\mathbf { R } = \left[ \begin{array} { c c c | c } 1 & - 3 & 0 & - 5 \\- 2 & 1 & 5 & 1 \\5 & 0 & 1 & - 4\end{array} \right]$ write the matrix obtained after executing the following elementary row operations: i). First, multiply the first row by 2 and add the result to the second row. Ii)) Then, multiply the first row by -5 and add the result to the third row.

Consider the matrix below. (a) Determine the order of the matrix. (b) Determine the order of the matrix and determine if the matrix is a row matrix, a column matrix, a matrix, or none of these. $\left[ \begin{array} { c c c c } - 4 & 1 & 8 & 0.8 \\6.1 & 1 & 0 & 3 \\- 1 & - 0.9 & 5 & - 1\end{array} \right]$

To reach a sales meeting, Carrie traveled by plane for 1 hour and by car for an additional 2 hours. The plane travels 82 mph faster than the car. If the total distance traveled is 217 miles, what are the Speeds of the plane and the car? (Assume that the plane and the car travel at constant rates.)

It takes a barge 1 hour to travel 8 miles downstream with the current and 4 hours to return against the current. Find the speed of the barge in still water and the speed of the current.

Solve the system by the addition method. 3x + 7y = -20 -3x + 6y = -6

Two trains leave the depot at the same time, one traveling east and the other traveling west. The speed of one train is 14 mph slower than the other. If after 3 hours the distance between the trains is 150 miles, find the speed of each train.

The small zoo at Nichols Park charges $9 for adult admission, $6 for child admission (18 years old and under), and $4 for senior admission (60 years old and over). For one day, the zoo collected $573 And admitted 87 visitors. If the adult admission is 7 more than the senior admission, how many Persons of each category were admitted on this particular day?

Solve by using either the addition method or the substitution method. 2(5y-2)-6x=5-x x+y=-(-18+y)

Determine the order of the matrix. $\left[ \begin{array} { l l } 6 & 6 \\6 & 6 \\0 & 0\end{array} \right]$