Algebra Know-It-ALL

328 Review Questions and Answers

2 x+ 8 = (1/3)x+ 3

6 x+ 24 =x+ 9

6 x+ 15 =x

5 x+ 15 = 0

5 x=− 15

x=− 3

Question 16-4

How can we put the two-by-two linear system from Question 16-2 into a pair of SI equations

withx all by itself on the left sides of the equals signs?

Answer 16-4

For the first original equation, we can do this:

2 x−y+ 8 = 0

2 x+ 8 =y

2 x=y− 8

x= (1/2)y− 4

and for the second original equation, we can do this:

x− 3 y+ 9 = 0

x+ 9 = 3 y

x= 3 y− 9

Question 16-5

How can we combine the two equations from Answer 16-4 to get a first-degree equation and

solve the original system for y?

Answer 16-5

We can mix the right sides of the two SI equations together and then solve the resulting first-

degree equation in y by manipulation, as follows:

(1/2)y− 4 = 3 y− 9

y− 8 = 6 y− 18

y+ 10 = 6 y

10 = 5 y

y= 2

Question 16-6

How can we be sure the solution we obtained in Answers 16-3 and 16-5 is in fact the correct

solution to the original two-by-two linear system?