Exam 9: Prelude to Calculus

An ad for a snack consisting of peanuts and raisins states that one serving of the regular snack contains 10 peanuts and 25 raisins and has 110 calories. The lite version of the snack consists of 5 peanuts and 30 raisins per serving and, according to the ad, has 97 calories. How many calories are in each peanut and each raisin?

Use Gaussian elimination to find all solutions to the given system of equations. Work directly with equations rather than matrices.

Find a number b such that the system of linear equations has no solutions. Give the exact answer.

The system of linear equations has no solutions if and only if b = 12 or b = 0.

At an educational district's office, three types of employee wages are incorporated into the budget: specialists, managers, and directors. Employees of the same classification earn the same wage district wide. At one location, there are 15 specialists, 5 managers, and 2 directors with a total annual salary budget of $1,070,000. At another location, there are 15 specialists, 2 managers, and 1 director with a total annual salary budget of $771,000. A third location has 14 specialists, 1 manager, and 2 directors with a total annual salary budget of $667,000.

The system of linear equations has no solutions if and only if b = 5 or b = 0.

The system of linear equations has infinitely many solutions.

The solution of the following system of equations is given by x = 1, y = -1, z = 4.

Find all solutions to the given system of equations.

Represent the given system of linear equations as a matrix. Use alphabetical order for the variables. 6x+6y-9z =-6 4x-y+8z =4 8x+4y+z =-9

Find a number b < 49 such that the system of linear equations has infinitely many solutions.

Interpret the given matrix as a system of linear equations. Use x for the first variable, y for the second variable, and z for the third variable.

The system of linear equations has infinitely many solutions.

Find a number b such that the system of linear equations has no solutions. Give the exact answer.

Find a number b such that the system of linear equations has no solutions. Give the exact answer.

Determine the value of x in the given system of linear equations. x+2y-z =4 -2x-2y+2z =-3 -3x-2y-4z =3

Interpret the given matrix as a system of linear equations. Use x for the first variable, y for the second variable, and z for the third variable.

Find all solutions to the given system of equations.

Find all solutions to the given system of equations.

Use Gaussian elimination to find all solutions to the given system of equations. Work directly with equations rather than matrices.