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 20y = -5x (a) Is the system inconsistent, or are the equations dependent, or neither? (b) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line? (c) Does the system have one solution, no solution, or an infinite number of solutions? (a) Is the system inconsistent, or are the equations dependent, or neither? Inconsistent system Dependent equations (b) Describe the graph. Parallel lines Intersecting lines (c) Determine the number of solutions. Infinite solutions One solution

Explanation / Answer

x+4y = 0 can be written as x = -4y

Second equation is 20y = -5x or x = = - 4y when 5 is taken common.

So, both equations are same.

a) These are dependent equations. If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

b) Graph is one line as both equations are same.

c) Infinite number of solutions.

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