18. solve using the elimination method.?

I guess the equations are (you forgot an "x" in the second equation) :

0.05x + 0.25y = 66

0.15x + 0.05y = 72

The purpose of eliminating method is to eliminate a variable. Here, we can multiply first equation by -3 to eliminate x or multiply second equation by -5 to eliminate y. Let's say we eliminate x.

Equation 1 multiplied by -3 equal :

-0.15x - 0.75y = -198

Add it to second equation :

-0.15x + 0.15x - 0.75y + 0.05y = -198 + 72

x are eliminated :

-0.7y = -126

y = -126/-0.7

y = 180

Replace it in any equation. Let's say the first one :

0.05x + 0.25y = 66

0.05x + 0.25*(180) = 66

0.05x + 45 = 66

0.05x = 66 - 45

0.05x = 21

x = 21/0.05

x = 420

So x = 420 and y = 180

PROOF :

0.05x + 0.25y = 66

0.05*(420) + 0.25*(180) = 66

21 + 45 = 66

66 = 66 :ok

0.15x + 0.05y = 72

0.15*(420) + 0.05*(180) = 72

63 + 9 = 72 :ok