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Chapter 5: Q. 337 (page 678)

In the following exercises, without graphing determine the number of solutions and then classify the system of equations.

5x-4y=0y=54x-5

Short Answer

Expert verified

The system is inconsistent and has no solution.

Step by step solution

01

Step 1. Given information

The given system is5x-4y=0y=54x-5.

02

Step 2. Equate the ratio of coefficients and constants

  • Write both the given equations in standard form.

5x-4y=0-5x+4y=-5

  • Check if the ratios of the coefficients of xand yare equal.

5-5=?-44-1鈮�-1

  • Thus the two lines are either parallel or coincident.
  • Now, check if the ratio of the constant term is also equal to the ratio of coefficients.

-1=?0-5-1鈮�0

  • As the ratios are not equal, the lines are parallel.
  • The system is inconsistent.

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