1/2x+1/3y=7,1/4x+2/3y=6

what is the solution of the system shown?

a. (1/6,14)
b. (6/12)
c. (10 2/3,5)

We can see that 1/3 times 2=2/3
we can cancel the y terms

multily first equation by -2 and add to 2nd

-x-2/3y=-14
1/4x+2/3y=6 +
-3/4x+0y=-8

-3/4x=-8
times both sides by -4
3x=32
divide both sides by 3
x=32/3

sub back

1/2x+1/3y=7
1/2(32/3)+1/3y=7
16/3+1/3y=7
times 3 both sides
16+y=21
minus 16 both sides
y=5

(32/3,5)
(10 and 2/3,50

C is answer
an easier way would be to get rid of the fractions by multiplying the first equation by 6 and 2nd one by 12 but oh well

C is the answer