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Chapter 5: Q 5.20. (page 591)

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

x+4y=12-x+y=3

Short Answer

Expert verified

The system of the equation has 1 solution and is consistent and independent.

Step by step solution

01

Step 1. Given information 

The system of equations is

x+4y=12-x+y=3

02

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

The first equation is

x+4y=12

Solve for y

x+4y=12x+4y-x=12-x4y=-x+124y4=-14x+124y=-14x+3

Compare with the slope-intercept formula of line

y=mx+b

So,

m=-14b=3

03

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

The second equation is

-x+y=3

Solve for y

-x+y=3-x+y+x=3+xy=x+3

Compare with the slope-intercept formula of line

y=mx+b

So,

m=1b=3

04

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

First equation:

Slope is -14

y-intercept is 3

Second equation:

Slope is 1

y-intercept is 3

Since the slopes are different, the lines intersect.

A system of equations whose graphs are intersecting has 1 solution and is consistent and independent.

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