Solve the following system by the elimination method.
1/5x+y=6/5
1/10x+1/3y=9/10

Eqn 1. (1/5)x+y=(6/5)
eqn 2. (1/10)x+(1/3)y=(9/10)

eqn 1. (0.2)x+y=(1.2)
eqn 2. (0.1)x+(0.333)y=(0.9)

1st. multiply eqn 1. by (-1/2)
=
[(1/5)x+y=(6/5)] × (-1/2) = (-0.1)x + (-0.5)y = (-0.6)

(-0.1)x + (-0.5)y = (-0.6)
(0.1)x + (0.3333)y = (0.9)

now add the 2 equations together

and the x term will cancel out leaving...

(-0.1666)y = 0.3

y = 0.3÷(-0.1666) = -1.8

plug y=-1.8 into eqn 1 or eqn 2

0.2 x +(-1.8) = 1.2

x = (1.2+1.8)÷ 0.2 = 15