These values should be checked by plugging them into both of the original equations to be sure they’re
correct. Here we go:
x+y= 990
870 + 120 = 990
990 = 990
and
x − y= 750
870 − 120 = 750
750 = 750
We can now state these solutions with confidence, at least until the wind changes or the airplane alters its
cruising speed!
Double Elimination
There’s another way to solve two-by-two systems of linear equations, which I like to call
double elimination. It’s also called the addition method. We can morph one or both equations
so that when we add them in their entirety, one of the variables disappears. That allows us to
solve for the other variable. We can then do the same thing to make the other variable disap-
pear, and solve for the one!
Get in the same form
Let’s solve the following two-by-two linear system using double elimination, first for u (by
eliminatingt) and then for t (by eliminating u):
2 t+ 5 u=− 7
and
u= 4 t− 3
Before we go any farther, we must get both equations in the same form. Let’s use the form
of the first equation. The second equation can be morphed into that form by subtracting 4t
from each side, getting
− 4 t+u=− 3
Eliminate the first variable
Our first objective is to make t vanish when we add multiples of the equations. We can mul-
tiply the first original equation through by 2, getting
4 t+ 10 u=− 14
Double Elimination 255
