To find the error that Carolyn made, we proceed to solve the problem as follows:
3x - 2y = 7
-x + y = 2
We solve for the constants and now, we operate in such a way we will have just one variable, that is:
3x - 2y = 7
3(-x + y) = 3(2)
Then, we add them:
3x - 2y = 7
-3x +3y = 6
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3x + (-3x) -2y + (3y) = 7 + 6
Then we solve for y:
=> y = 13
Now, we will replace that value in one of our expressions, that is:
3x -2(13) = 7 => 3x = 33 => x = 11.
From this, we have that the point for which the system is true is (11, 13).
Now, going back to the procedure of Carolyn, we can deduce that she took the second function as if it were equivalent to the value of y in the first function; but the correct way to solve the problem is by operating them as separate functions [Since it is not stated that the second function is equivalent to the value of y in the first one], and the way it is solved is by multiplying values in order to solve for a sum or subtraction, or by replacing the values in an array[Linear Algebra].