Algebra Know-It-ALL

6. To use the morph-and-mix method, we must get the equations into SI form. We’re told
   to treat x as the dependent variable, so we must isolate x on the left sides of the equals
   signs. The equations morph like this:

− 37 x− 4 y= 35

− 37 x= 4 y+ 35

x= (−4/37)y− 35/37

and

− 10 x+ 17 y= 8

− 10 x=− 17 y+ 8

x= (17/10)y− 8/10

Now we mix the right sides to get

(−4/37)y− 35/37 = (17/10)y− 8/10

It will simplify things if we can get a common denominator. Let’s multiply the numera-

tors and denominators on the left side of this equation by 10, and multiply the numera-

tors and denominators on the right side by 37. That gives us

(−40/370)y− 350/370 = (629/370)y− 296/370

Multiplying this entire equation through by 370, we obtain an equation without frac-

tions, which we can solve in steps as follows:

− 40 y− 350 = 629 y− 296

− 40 y= 629 y+ 54

− 669 y= 54

y=−54/669

=−18/223

This agrees with the solution we obtained in the chapter text. Now we can plug this into

either of the SI equations we derived earlier. Let’s use the second one. We get

x= (17/10)y− 8/10

= (17/10) × (−18/223)− 8/10

=−306 / 2,230 − 8/10

=−306 / 2,230 − (8 × 223) / (10 × 223)

=−306 / 2,230 − 1,784 / 2,230

=−2,090 / 2,230

=−209/223

This, too, agrees with the result we obtained in the chapter text.

Chapter 18 653