Solving the System of Linear Equations
If (x,y,z) = (α,β,γ) is the unique solution of the system of simultaneous linear equations:
3x - 4y + 2z + 7 = 0, 2x + 3y - z = 10, x - 2y - 3z = 3,
then α = ?
A battery of emf \( E \) and internal resistance \( r \) is connected to a rheostat. When a current of 2A is drawn from the battery, the potential difference across the rheostat is 5V. The potential difference becomes 4V when a current of 4A is drawn from the battery. Calculate the value of \( E \) and \( r \).