Exam 8: Systems of Linear Equations and Inequalities

Perform the indicated operations for the expression, if possible.

Solve the system of linear equations for a, b, and c.

Find the partial-fraction decomposition for the rational function.

Find the value of the objective function z = 5x - 6y at each of the vertices (-1, -2), (-9, -3), and (7, -2), and then state the maximum and minimum values of the function.

Solve the system of linear equations using Gauss-Jordon elimination with back-substitution. -9x - 6y = 6 -7x + 6y = 26

Apply determinants to find the area of a triangle with vertices (-2, 12), (-4, 5), and (-8, -4).

Find the value of the objective function z = 6x + 4y at each of the vertices (4, 3), (-3, -7), (-3, 7) (9, -6), and then state the maximum and minimum values of the function.

Use Cramer's Rule to solve the system of equations. 2r + 8s + t = 12 R + 2s + t = 4 7r - s + t = 13

Find the inverse of the matrix.

Evaluate the 3 x 3 determinant.

Evaluate the determinant.

Solve the system of linear equations by graphing the following equations. -8x + 8y = -16 -7x + 2y = 16

Find A^-1 given that

Write the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

Graph the system of inequalities.

Write the matrix in row echelon form.

Write the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

A candy company mixes chocolate and peanuts to create one of their signature confections. How many pounds of chocolate costing $13.50 per pound must be mixed with peanuts costing $3.69 per pound to create 60 pounds of mixture that costs $662.85? Let c represent the number of pounds of chocolate and p represent the number of pounds of peanuts.

Solve the system of linear equations by graphing the following equations. 4x - 6y = -52 -5x + 5y = 55

Maximize