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Algebra Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The simultaneous equations (1) and (2) have at least two distinct (x,y)(x, y) solutions. 2x+5y=ab2x + 5y = a - b (1) 4x+10y=a+b4x + 10y = a + b (2) The simultaneous equations (3) and (4) also have at least two distinct (x,y)(x, y) solutions. 3x2y=ab+43x - 2y = a - b + 4 (3) 9x6y=a+4b19x - 6y = a + 4b - 1 (4) What is the value of 10a+b10a + b?

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