please help!!! Which ordered triple represents all of the solutions to the system of equations shown below?2x - 2y - z = 6-x + y + 3z = -33x - 3y + 2z = 9a(-x, x + 2, 0)b(x, x - 3, 0)c(x + 2, x, 0)d(0, y, y + 4)What is the solution to the system of equations shown below?2x - y + z = 44x - 2y + 2z = 8-x + 3y - z = 5a (5, 4, -2)b (0, -5, -1)c No Solutiond Infinite Solutions
Accepted Solution
A:
Answer: b (x, x - 3, 0)d Infinite SolutionsStep-by-step explanation:1. A graphing calculator or any of several solvers available on the internet can tell you the reduced row-echelon form of the augmented matrix ... [tex]\left[\begin{array}{ccc|c}2&-2&-1&6\\-1&1&3&-3\\3&-3&2&9\end{array}\right][/tex]is the matrix ...[tex]\left[\begin{array}{ccc|c}1&-1&0&3\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]The first row can be interpreted as the equation ... x -y = 3 x -3 = y . . . . . add y-3The second row can be interpreted as the equation ... z = 0Then the solution set is ... (x, y, z) = (x, x -3, 0) . . . . matches selection B__2. The second equation is 2 times the first equation, so the system of equations is dependent. There are infinite solutions.