Solve the following simultaneous equations: (1/3)x + y = 10/3; 2x + (1/4)y = 11/4

Answer: \((x, y) = (1, 3)\)

Let \(\frac{1}{3}x + y = \frac{10}{3}\) ... (I) and \(2x + \frac{1}{4}y = \frac{11}{4}\) ... (II).

Multiply equation (I) by 3 to clear fractions:\[x + 3y = 10\]

Multiply equation (II) by 4 to clear fractions:\[8x + y = 11\]

Multiply (II) by 3: \(24x + 3y = 33\)

Subtract the equations to eliminate \(y\):\[-23x = -23\]\[x = 1\]

Substitute \(x = 1\) in (I) cleared of fractions: \(3y = 10 - 1 = 9\), so \(y = 3\).

Check in (II): \(2(1) + \frac{1}{4}(3) = \frac{11}{4}\), which is true.