Pre-Algebra Demystified

208 CHAPTER 11 Graphing

xþ2y¼ 6

2 þ 2 ð 2 Þ¼ 6

2 þ 4 ¼ 6

6 ¼ 6

Another solution to the equation xþ2y¼6 is (4, 1), since

xþ2y¼ 6

4 þ 2 ð 1 Þ¼ 6

4 þ 2 ¼ 6

6 ¼ 6

The linear equation xþ2y¼6 actually has aninfinitenumber of solutions.

For any value of x, a corresponding value of y can be found by substituting the

value for x into the equation and solving it for y. For example, if x¼8, then

xþ2y¼ 6

8 þ2y¼ 6

8 
 8 þ2y¼ 6 
 8

2y¼
 2

2y

2

¼

2

2

y¼
 1

When x¼8, y¼
1 and the ordered pair (8,
1) is a solution, too.

EXAMPLE

Find a solution to the equation 3x
y¼10.

SOLUTION

Select any value for x, say x¼4, substitute in the equation, and then solve

for y:

3x
y¼ 10

3 ð 4 Þ
y¼ 10

12 
y¼ 10

12 
 12 
y¼ 10 
 12


y¼
 2


1y


 1

¼

2

1

y¼ 2