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When the coefficients of the variables in the linear equations are different.

If

eqn(A): ax + by+ cz + ... = m, and

eqn(B): px + qy + rz + ... = n

where x, y z are variables and the rest are constants, then

p*eqn(A) = pax + pby+ pcz + ... = pm and

a*eqn(B) = apx + aqy + arz + ... = an

The coefficients of x, pa and ap, are equal and so subtracting one equation from the other will eliminate x.

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