# Equation System – Math 1324 Exam 3

### Equation System – Math 1324 Exam 3

The key terms in this Math course include Equation System.

Use graphical methods to solve the linear programming problem.
Maximize z = 8x + 12y
subject to: 40x + 80y ≤ 560
6x + 8y ≤ 72
x ≥ 0
y ≥ 0

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Maximum of 92 when x = 4 and y = 5

Maximum of 96 when x = 9 and y = 2

Maximum of 100 when x = 8 and y = 3Correct

Maximum of 120 when x = 3 and y = 8

Determine whether the given ordered set of numbers is a solution of the system of equations.(-2, -1, 3)
4x – 4y + z = -1

5x + 5z = 5

x + 4y – 2z = -12

YesCorrect!

No

Solve the system of two equations in two variables.
5x + 9y = 43
-2x – 7y = -24

(4, 3)

(5, 2)Correct!

No solution

(5, 3)

#### Equation System – Math 1324 Exam 3

Obtain an equivalent system by replacing the third equation by the sum of itself and -1 times the second equation.
x – 2y – 7z = 17
-6x + 4y + 5z = -9
8x + 7y – z = -4

x – 2y – 7z = 17
-6x + 4y + 5z = -9
-14x – 3y + 6z = 5

x – 2y – 7z = 17
-6x + 4y + 5z = -9
2x + 11y + 4z = -13

x – 2y – 7z = 17
-6x + 4y + 5z = -9 –Correct
14x + 3y – 6z = 5

x – 2y – 7z = 17
14x + 3y – 6z = 5
8x + 7y – z = -4

Write an augmented matrix for the system of equations.
9x + 9z = 54
-2y + 8z = 2
7x + 7y + 3z = 83

Perform row operations on the augmented matrix as far as necessary to determine whether the system is independent, dependent, or inconsistent.

x + y + z = -1
x – y + 3z = -5
3x + y + z = -3

Inconsistent

IndependentCorrect

Dependent

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