
Steps  Solution  
1.  Add both the equations, and reduce by common factors.  In this case, we get: 5x + 5y = 25, which has 5 as common term. So, we get: x + y = 5 

2.  Subtract one from the other, and reduce by common factors.  In this case, we get: x  y = 1, with no common factor 

3.  Add and Subtract the two new equations again to get the answer.  In this case, adding them again gives: 2x = 6 or, x = 3 And subtracting, we get: 2y = 4 or, y = 2 Thus, we get: x = 3, y = 2, which is the answer! 
Adding, we get: 68x  68y = 204 or, x  y = 3 Subtracting, we get: 22x + 22y = 22 or, x + y = 1 Adding again, 2x = 4; or, x = 2 Subtracting again, 2y = 2; or, y = 1 Thus, the solution is: x = 2, y = 1 
Adding, we get: 2431x  2431y = 2431 or, x  y = 1 Subtracting, we get: 1479x + 1479y = 7395 or, x + y = 5 Adding again, 2x = 4; or, x = 2 Subtracting again, 2y = 6; or, y = 3 Thus, the solution is: x = 2, y = 3 
Consider two equations, ax + by = c bx + ay = d Adding, (a + b)x + (b + a)y = c + d or, x + y = (c + d)/(a + b) Subtracting, (a  b)x + (b  a)y = c  d or, (a  b)x  (a  b)y = c  d or, x  y = (c  d)/(a  b) Adding again, we get: (c+d) (cd) 2x =  +  (a+b) (ab) Subtracting again, we get: (c+d) (cd) 2y =    (a+b) (ab) Note that, dividing both the equations by 2 provides the solution. 
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