If elimination of a variable from a pair of linear equations leads to the statement 0 = 7, then the system has:

**Steps**:
1. Multiply one or both equations by chosen numbers so coefficients of ONE variable become equal (in magnitude).
2. Add or subtract to ELIMINATE that variable.
3. Solve the resulting one-variable equation.
4. Plug back to find the other.

**Example**: $3x+4y=10$; $2x-3y=-1$.
- Multiply first by 3, second by 4: $9x+12y=30,8x-12y=-4$.
- Add: $17x=26$ → $x=26/17$. Substituting back gives $y$.

Elimination is faster than substitution when both equations have non-trivial coefficients.