Question 174784
I'm not sure what you mean by the "addition method" but I would solve the system of linear equations by attenpting to eliminate one of the unknowns.

Multiply 3x-2.5y=7.125 by 2.5 (Equation #1)
 and multiply 2.5x-3y=7.3125 by 3 (Equation #2)

We have 2.5*(3x-2.5y*)=2.5*(7.125)
        2.5*3*x - 2.5*2.5*y = 2.5*3*x-6.25*y = 17.8125 (#1)

and 3*2.5*x - 3*3*y = 3*7.3125* = 21.9375 (#2)

Subtract #2 from #1

-6.25*y + 9*y = 17.8125-21.9375

So 2.75*y = -4.125 or y = -4.125/2.75 = -1.5

Substitute -1.5 for y in equation #1
3*x - 2.5*(-1.5)=7.125
3*x + 3.75 = 7.125
3*x = 7.125 - 3.75 = 3.375
There x = 3.375/3 = 1.125

Check results

Using equation #1

3*(1.125)-2.5*(-1.5) = 3.375+3.75=7.125 (solution checks)