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