How do you find the solution of the system of equations #3xy=1# and #x+y=3#?
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To find the solution of the system of equations (3x  y = 1) and (x + y = 3), you can use the method of substitution or elimination.
Method 1: Substitution

Solve one of the equations for one variable. Let's solve the second equation for (y): (y = 3  x)

Substitute the expression for (y) into the first equation: (3x  (3  x) = 1)

Simplify the equation: (3x  3 + x = 1)
(4x  3 = 1)
(4x = 4)
(x = 1) 
Substitute the value of (x) back into the second equation to find (y): (y = 3  1)
(y = 2)
So, the solution to the system of equations is (x = 1) and (y = 2).
Method 2: Elimination

Add the two equations together to eliminate (y): (3x  y + x + y = 1 + 3)
(4x = 4)
(x = 1) 
Substitute the value of (x) back into one of the original equations to find (y): (1 + y = 3)
(y = 2)
Again, the solution is (x = 1) and (y = 2).
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