elimination method 5x + 6y = -75x - 3y = 146

what is this... Your teacher did not give it to you this way.

did you mean
5x+6y=-75
x-3y=146 ?

if so, multiply the second equation by 2
5x+6y=-75
2x-6y=292
add the equations

7x=217
x= 31

9x-y=3 elimination method