Question 251998
There are multiple ways to solve this system of equations.  One method is to graph the two functions and find out where they intersect.  Another method is to solve using substitution.  A third method is to solve using elimination.  A fourth method is to solve using a matrix, but I don't think that is the one you will be using right now.
The method of choice for this type of problem is elimination.
2x-2y=4
3y-x=1
Step 1, get the variables in the same columns (get x under x, y under y, constant(the number without a variable)under constant).
so
2x-2y=4
-x+3y=1
Step 2, multiply everything in one equation by a number that will allow one of the variables in that equation to be opposite the same variable in the other equation.  In this example, we will multiply the second equation by 2 so that we get -2x (which is opposite 2x)
2(-x+3y=1)
distribute the 2
-2x+6y=2
Step 3, add the equations
2x-2y=4
-2x+6y=2
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0+4y=6
or y=3/2
now plug 3/2 in for y in one of the original equations and you get
2x-2(3/2)=4  Solve for x
2x-3=4
2x=7
x=7/2
so your solution is the point (x,y)=(7/2,3/2)
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