How do you find the solution of the system of equations #3x-y=1# and #x+y=3#?

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

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

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

3. Simplify the equation: (3x - 3 + x = 1)
   (4x - 3 = 1)
   (4x = 4)
   (x = 1)

4. 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

1. Add the two equations together to eliminate (y): (3x - y + x + y = 1 + 3)
   (4x = 4)
   (x = 1)

2. 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).