Algebra Know-It-ALL

Check! Finally the fourth:

y= 4 x+ 1

1 = 4 × 0 + 1

1 = 0 + 1

1 = 1

We can now be confident that the solution to the system is indeed x= 0 and y= 1.

10. Figure B-10 shows graphs of all four equations on the Cartesian plane. It’s visually
    apparent that if we choose any pair or triplet of these lines, they intersect at the point
    (0, 1) and nowhere else. Therefore, any pair or triplet of the equations, taken as a two-
    by-two or three-by-two linear system, has the unique solution x= 0 and y= 1.

Chapter 19

1. Here are the original three equations, stated again for convenience, followed by the
   step-by-step processes that get the equations into form for conversion to a matrix:

x=y−z− 7

y= 2 x+ 2 z+ 2

z= 3 x− 5 y+ 4

Each axis

increment

is 1 unit

y= –x+ 1

y= –2x+ 1

y= 3x+ 1

y= 4x+ 1

x

y

(0,1)

Figure B-10 Illustration for the solution to Prob. 10

in Chap. 18.

Chapter 19 655