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Chapter 5: Q 5.17. (page 590)

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

y=-2x-44x+2y=9

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=-2x-44x+2y=9

02

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

The first equation is

y=-2x-4

Compare with the slope-intercept formula of line

y=mx+b

So,

m=-2b=-4

03

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

The second equation is

4x+2y=9

Solve for y

4x+2y-4x=9-4x2y=-4x+92y2=-4x2+92y=-2x+92

Compare with the slope-intercept formula of line

y=mx+b

So,

m=-2b=92

04

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

First equation:

Slope is -2

y-intercept is-4

Second equation:

Slope is -2

y-intercept is 92

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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