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

A is the answer (1/16,14)