Find (X-Y) if 4x - 3y = 7 and 3x - 2y = 5

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.

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