Find the value of (y) from (2x+5y=31) and (2x+y=15).

Correct answer: (y=4)

Both equations contain the identical term \(2x\). Subtracting the second equation from the first cancels this term, leaving an equation only in y. This is an efficient use of the elimination method because the coefficients of x already match exactly; no multiplication of either equation is required.

Compute \((2x+5y)-(2x+y)=31-15\). The x terms cancel, and \(5y-y=4y\), so \(4y=16\). Dividing by 4 gives \(y=4\). For a check, the second equation becomes \(2x+4=15\), so x=\(11/2\); inserting these values into the first gives \(11+20=31\). Thus y=4 and option B is correct. The useful observation is to remove the equal \(2x\) terms directly.