Algebra Know-It-ALL

Two versions of the SI form

In a two-by-two system, it often doesn’t matter which variable we consider independent and
which one we consider dependent. But a true SI equation always has the dependent variable
alone on the left side of the equals sign, and the independent variable on the right side along
with constants that represent characteristics of a graph. For example, if we see the equation

x−y= 10

then we can say that both of the following are SI equivalents of it:

y=x− 10

and

x=y+ 10

In the first case, we treat y as the dependent variable. In the second case, we treat x as the
dependent variable.

Are you confused?

Once you’ve solved a two-by-two linear system (or think you have), you should consider your solutions
tentative until you’ve plugged them into both of the original equations and worked out the arithmetic to
be sure that they’re correct. The solution to the system originally stated on page 251 appears to be x= 5
andy=−6. Is it, really? Check the first original equation:

8 x+ 4 y= 16

8 × 5 + 4 × (−6)= 16

40 − 24 = 16

16 = 16

That checks out fine! Now for the second original equation:

7 x−y= 41

7 × 5 − (−6)= 41

35 + 6 = 41

41 = 41

It works out here, too! You can now be confident that the solutions are right.

Here’s a challenge!

While flying directly into a high-altitude wind, an airplane has a groundspeed (speed measured with respect
to the earth) of 750 kilometers per hour (km/h). When flying right along with that same wind at the same
airspeed (speed measured with respect to the surrounding air), the plane has a groundspeed of 990 km/h.
What is the airspeed of the plane? What is the speed of the wind relative to the earth?

Morph and Mix 253