On solving (4x+3y=50) and (2x-5y=-6), what is the value of (y)?

Correct answer: (y=\frac{62}{13})

The direct answer is option D: \(y=\frac{62}{13}\). We need to solve both equations together. The second equation is \(2x-5y=-6\). Move \(-5y\) to the other side: \(2x=5y-6\), so \(x=\frac{5y-6}{2}\). Substitute this into \(4x+3y=50\): \(4\left(\frac{5y-6}{2}\right)+3y=50\). This becomes \(2(5y-6)+3y=50\), so \(10y-12+3y=50\), hence \(13y=62\), and \(y=\frac{62}{13}\). Option A, \(\frac{52}{13}\), does not satisfy the equations. Option B, \(\frac{56}{13}\), is also not the value obtained after simplification. Option C, \(\frac{58}{13}\), is another nearby but incorrect numerator. Option D is correct; substituting it gives the corresponding value of \(x\) and both original equations are satisfied. A useful check is to substitute the final value back into at least one equation. Keep signs carefully when moving a term across the equal sign.