Equivalent equations help you to knock out the choices and solve the problems more easier.
for example
x + 6y = 8
2x + 4y = 8
multiply first equation to get rid of from x
2x+12y=16
2x+4y=8
now subtract second equation from first
8y=8
y=1
now put value of y in seond equation
2x+4(1)=8
2x=8-4
2x=4
x=2
hence,
equivalent equations help you to solve a system of equations