Without graphing, answer the questions for the following linear system. x + 4y =

Question

Without graphing, answer the questions for the following linear system. x + 4y = 0 16y = - 4x Is the system inconsistent, or are the equations dependent, or neither? Is the graph a pair of intersecting lines, a pair of parallel lines, or one line? Does the system have one solution, no solution, or an infinite number of solutions? Is the system inconsistent, or are the equations dependent, or neither? Neither Inconsistent System Parallel lines Intersecting lines Infinite solutions No solution Dependent equations Describe the graph. One line Determine the number of solutions. One solutions

Explanation / Answer

The system of equations

                                              X+4Y=0..................(1)

                                                  -16Y = 4x.............(2)

(a) the system is consistent. (there are non-zero solutions y=1,x=-4).

The equations are dependent ((2) is just 4x (1))

(b) Graph is that of one line ((1) and (2) represent identical straight lines)

(c) The system has infinite solutions (y =k, x =-4k for any value of k is a solution)

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