We are given the following simultaneous equations: \(4x - 3y = 7 \quad \text{(Equation 1)}\) \(3x - 2y = 5 \quad \text{(Equation 2)}\) To eliminate \(y\), we multiply Equation 1 by 2 and Equation 2 by 3: \(2(4x - 3y) = 2(7) \implies 8x - 6y = 14 \quad \text{(Equation 3)}\) \(3(3x - 2y) = 3(5) \implies 9x - 6y = 15 \quad \text{(Equation 4)}\) Now we subtract Equation 3 from Equation 4: \((9x - 6y) - (8x - 6y) = 15 - 14\) \(x = 1\) Substituting \(x = 1\) into Equation 2: \(3(1) - 2y = 5\) \(3 - 2y = 5\) \(-2y = 2 \implies y = -1\) Now we have \(x = 1\) and \(y = -1\). Thus, \(X - Y = x - y = 1 - (-1) = 1 + 1 = 2\) Therefore, the value of \(X - Y\) is: 2.