Check mesh algebra with source power

Two clockwise mesh currents satisfy 4i₁ − i₂ = 7 and −i₁ + 3i₂ = 1, with resistances in ohms and source rises in volts. The meshes share a 1 Ω resistor in opposite directions. The remaining resistances are 3 Ω in mesh one and 2 Ω in mesh two.

What is the total resistor heating power?

Organize the givens & assumptions

Mesh equations: 4i₁ − i₂ = 7; −i₁ + 3i₂ = 1
Shared resistor: 1 Ω
Unshared resistors: 3 Ω and 2 Ω

Settled lumped DC circuit, ideal connecting wires, positive constant Ohmic resistances and no changing external magnetic flux. Sources are ideal except for explicitly specified series resistances.

A $14\ \mathrm W$
B $15\ \mathrm W$
C $19\ \mathrm W$
D $23\ \mathrm W$

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