Find the two values of y which satisfy the simultaneous equation 3x + y = 8, x(^2) + xy = 6.
-
A.
-1 and 5 -
B.
-5 and 1 -
C.
1 and 5 -
D.
1 and 1
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})