Solve for I2 from the pair of equations 4I1 + 4I2 = 2 and 6I1 + 7I2 = 4 (state the correct magnitude and sign in amperes).

Introduction / Context:
When analyzing circuits using mesh or nodal methods, you often end up with simultaneous linear equations for unknown currents. Solving cleanly and confirming the sign ensures the physical interpretation (direction) is correct.

Given Data / Assumptions:

• Equations: 4I1 + 4I2 = 2 and 6I1 + 7I2 = 4.
• Unknowns represent steady DC currents in amperes.
• Linear algebra methods (substitution/elimination) apply directly.

Concept / Approach:

Use substitution to isolate one variable and substitute into the other equation. Maintain unit consistency and sign discipline. The solution pair will satisfy both equations simultaneously.

Step-by-Step Solution:

Verification / Alternative check:

Back-solve I1: I1 = 0.5 − 1 = −0.5 A. Check: 6(−0.5) + 7(1) = −3 + 7 = 4, confirming the solution pair (−0.5, 1).

Why Other Options Are Wrong:

−1 A has the wrong sign; 100 mA and −100 mA are an order of magnitude too small relative to the equation scaling.

Common Pitfalls:

Sign errors when combining like terms, rounding prematurely, or not validating against both original equations.

Final Answer:

1 A