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Chapter 4: Q 26. (page 386)

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

y=32x+12x-3y=7

Short Answer

Expert verified

The number of solution is one and the system of equations is intersect lines, consistent and independent.

Step by step solution

01

Step 1. Given information.

The system of equations isy=32x+12x-3y=7.

02

Step 2. Solve the first equation for y and find the slope and y-intercept. 

Find the slope andy-intercept.

y=32x+1

Hence the slope is32and the y-intercept is 1.

03

Step 3. Solve the second equation for y and find the slope and y-intercept.

Find the slope and y-intercept.

2x-3y=73y=2x-7y=23x-73

Here the slope is 23and the y-intercept is -73.

04

Step 4. Explain the number of solutions.

  • Here the slopes are different.
  • The system of equation is intersected lines with one solution and that is consistent and independent.

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