Algebra Know-It-ALL

Part Two 327

• Solve the first-degree equation for x.


• Morph both equations into SI form with x all by itself on the left side of the
  equals sign.


• Mix the two equations to get a first-degree equation in y.


• Solve the first-degree equation for y.

Question 16-2

How can we put the following two-by-two linear system into a pair of SI equations with y all
by itself on the left side of the equals sign?

2 x−y+ 8 = 0

and

x− 3 y+ 9 = 0

Answer 16-2

By now, we’re good enough at equation manipulation to write down the steps one after
another, without having to justify everything. For the first original equation, we can
do this:

2 x−y+ 8 = 0

−y+ 8 =− 2 x

−y=− 2 x− 8

y= 2 x+ 8

and for the second original equation, we can do this:

x− 3 y+ 9 = 0

− 3 y+ 9 =−x

− 3 y=−x− 9

3 y=x+ 9

y= (1/3)x+ 3

Question 16-3

How can we combine the two equations from Answer 16-2 to get a first-degree equation and
solve the original system for x?

Answer 16-3

We can mix the right sides of the two SI equations together and then solve the resulting first-
degree equation in x by manipulation. Here it goes, one step at a time: