SOLUTION: how do I solve 1/2x+1/3y=3 3x+5y=36

Question 1014783: how do I solve 1/2x+1/3y=3
3x+5y=36

Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Use substitution, multiply the first equation by 6.

Now substitute into the second equation,

Then,

.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
I think you mean x/2 + y/3 = 3
1) x/2 + y/3 = 3
The GCF is 6
3x + 2y = 18
solve for x
x = (18 -2y) / 3
:
2) 3x + 5y = 36
substitute for x
(3 * (18 -2y) / 3) +5y = 36
((54 -6y) / 3) +5y = 36
GCF is 3
54 -6y +15y = 108
9y = 54
y = 6
:
now substitute for y in equation 2
3x + 30 = 36
3x = 6
x = 2
:
our solution is x=2 and y=6
now check the solution by substituting in equation 1)
:
2/2 + 6/3 = 3
1 + 2 = 3
3 = 3
our answer checks

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