Find the two values of y which satisfy the simultaneous equation 3x + y =…

Correct Answer: Option A

Explanation

(3x + y = 8 … (i))

(x^{2} + xy = 6 … (ii))

From (i), (y = 8 – 3x)

From (ii), (xy = 6 – x^{2} implies y = frac{6 – x^{2}}{x})

Equating the two values of y, we have

(8 – 3x = frac{6 – x^{2}}{x} implies x(8 – 3x) = 6 – x^{2})

(8x – 3x^{2} = 6 – x^{2} implies 6 – x^{2} – 8x + 3x^{2} = 0)

(2x^{2} – 8x + 6 = 0)

(x^{2} – 4x + 3 = 0)

(x^{2} – 3x – x + 3 = 0 implies x(x – 3) – 1(x – 3) = 0)

((x – 1)(x – 3) = 0 therefore text{x = 1 or 3})

(y = 8 – 3x )

When x = 1, (y = 8 – 3(1) = 5)

When x = 3, (y = 8 – 3(3) = -1)

(therefore text{y = -1 or 5})