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Chapter 4: Q 25. (page 386)

Without graphing, determine the number of solutions and then classify the system of equations.

y=23x+1-2x+3y=5

Short Answer

Expert verified

The number of solutions is 0 and the system of equations are parallel lines, inconsistent and independent.

Step by step solution

01

Step 1. Given information.

The system of equations isy=23x+1-2x+3y=5.

02

Step 2. Solve the first equation for y.

Find the slope andy-intercept.

y=23x+1

Hence the slope is 23and the y-intercept is 1.

03

Step 3. Solve the second equation for y.

Find the slope and y-intercept.

-2x+3y=5y=23x+53

Hence the slope is 23and the y-intercept is 53.

04

Step 4. Explain the number of solutions. 

  • Here the slopes are the same and y-intercepts are different.
  • The system of equations are parallel lines, inconsistent and independent and the number of solutions is 0.

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