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Chapter 5: Q 5.18. (page 590)

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

y=13x-5x-3y=6

Short Answer

Expert verified

The system of equations has no solution and is inconsistent and independent.

Step by step solution

01

Step 1. Given information 

The system of equations is

y=13x-5x-3y=6

02

Step 2. Find the slope and intercept of the first equation.

The first equation is

y=13x-5

Compare with the slope-intercept formula of line

y=mx+b

So,

m=13b=-5

03

Step 3. Find the slope and intercept of the second equation.

The second equation is

x-3y=6

Solve for y

x-3y=6x-6=3y3y=x-63y3=13x-63y=13x-2

Compare with the slope-intercept formula of line

y=mx+b

So,

m=13b=-2

04

Step 4. Compare the slopes and intercepts of the two lines.

First equation:

Slope is 13

y-intercept is -5

Second equation:

Slope is 13

y-intercept is 2

Since the slopes are the same and y-intercepts are different.

So, the lines are parallel.

A system of equations whose graphs are parallel lines has no solution and is inconsistent and independent.

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