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Chapter 5: Q 5.19. (page 591)

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

3x+2y=22x+y=1

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

3x+2y=22x+y=1

02

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

The first equation is

3x+2y=2

Solve for y

3x+2y=23x+2y-3x=2-3x2y=-3x+22y2=-32x+22y=-32x+1

Compare with the slope-intercept formula of line

y=mx+b

So,

m=-32b=1

03

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

The second equation is

2x+y=1

Solve for y

2x+y-2x=1-2xy=-2x+1

Compare with the slope-intercept formula of line

y=mx+b

So,

m=-2b=1

04

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

First equation:

Slope is -32

y-intercept is 1

Second equation:

Slope is -2

y-intercept is 1

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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