Algebra Know-It-ALL

338 Review Questions and Answers

Answer 18-6

Let’s multiply the top equation through by −3 and then add the bottom equation to it. This

gives us the sum

− 3 x− 9 z=− 27

3 x+ 13 z= 31

4 z= 4

This simplifies to the tentative solution z= 1.

Question 18-7

How can we solve the above two-by-two system for x by substituting in the solution for z we

obtained in Answer 18-6?

Answer 18-7

We can plug in the value 1 for z in either of the equations in the two-by-two system as stated

at the end of Answer 18-5. Let’s use the top equation. We have

x+ 3 z= 9

x+ 3 × 1 = 9

x+ 3 = 9

x= 6

Now we have the tentative solutions x= 6 and z= 1.

Question 18-8

Now that we know the values of x and z in the original three-by-three system, how can we

find the value of y?

Answer 18-8

We can plug in the value 6 for x and the value 1 for z in any of the original three equations, as

they are stated in Question 18-1. Let’s use the first one:

4 x= 8 + 4 y+ 4 z

4 × 6 = 8 + 4 y+ 4 × 1

24 = 8 + 4 y+ 4

20 = 8 + 4 y

12 = 4 y

3 =y

Now we have the complete, but still tentative, solution to the original three-by-three system:

x= 6

y= 3

z= 1