Beginning Algebra, 11th Edition

Any intersection point would be on both lines and would therefore be a solution of

bothequations. Thus, the coordinates of any point at which the lines intersect

give a solution of the system.

The graph in FIGURE 1shows that the solution of the system in Example 1(a)is

the intersection point Because two differentstraight lines can intersect at no

more than one point, there can never be more than one solution for such a system.

1 4, - 32.

SECTION 4.1 Solving Systems of Linear Equations by Graphing 249

x

y

0 2

3 x + 2y = 6

3

–2

4

x + 4y = –8

(4, –3)

The point of

intersection is

the solution of

the system.

FIGURE 1

x

y

0

2

(–1, 2)

5

5

3

4

3

• 2 x + 3y = 4

3 x – y = –5

FIGURE 2

Solving a System by Graphing

Solve the system of equations by graphing both equations on the same axes.

We graph these two lines by plotting several points for each line. Recall from

Section 3.2that the intercepts are often convenient choices.

2 x+ 3 y= 4 3 x-y=- 5

3 x- y=- 5

2 x+ 3 y= 4

NOW TRY EXAMPLE 2

EXERCISE 2
Solve the system by graphing.

2 x+y= 3

x- 2 y= 4

xy

0

20

8

• 
  

  (^23)
  4
  3
  xy
  05
  0

  
  


• 
  

  2 - 1
  -^53

  
  

The lines in FIGURE 2suggest that the graphs intersect

at the point We check this by substituting

for xand 2 for yin both equations.

CHECK First equation

Substitute.

✓ True

Second equation

Substitute.

✓ True

Because satisfies both equations, the solution

set of this system is 51 - 1, 2 26.

1 - 1, 2 2

- 5 =- 5

31 - 12 - 2 - 5

3 x- y=- 5

4 = 4

21 - 12 + 3122  4

2 x+ 3 y= 4

- 1

1 - 1, 2 2.

Find a third

ordered pair

as a check.

NOW TRY ANSWER

2. 51 2, - 126
   NOW TRY