Algebra Know-It-ALL

336 Review Questions and Answers

How can we put the first of these equations into the form ax+by+c=d, where a,b,c, and

d are constants?

Answer 18-1

Here are the steps we can take, one at a time, starting with the original equation:

4 x= 8 + 4 y+ 4 z

4 x− 4 y= 8 + 4 z

4 x− 4 y− 4 z= 8

Question 18-2

How can we put the second equation in Question 18-1 into the form ax+by+c=d, where

a,b,c, and d are constants?

Answer 18-2

Here are the steps we can take, one at a time, starting with the original equation:

2 y= 5 +x− 5 z

−x+ 2 y= 5 − 5 z

−x+ 2 y+ 5 z= 5

Question 18-3

How can we put the third equation in Question 18-1 into the form ax+by+c=d, where a,

b,c, and d are constants?

Answer 18-3

Here are the steps we can take, one at a time, starting with the original equation:

4 z= 13 − 2 x+y

2 x+ 4 z= 13 +y

2 x−y+ 4 z= 13

Question 18-4

Based on the rearrangements in Answers 18-1 through 18-3, how can we state the three-by-

three linear system from Question 18-1 now? What strategies can we use to solve it?

Answer 18-4

We can state the system by combining the final equations from Answers 18-1 through 18-3,

like this:

4 x− 4 y− 4 z= 8

−x+ 2 y+ 5 z= 5

2 x−y+ 4 z= 13