Question

If 2x + 3y = 13 and xy = 6​

Answer 1

Step-by-step explanation:

given,2x + 3y = 13

multiple by y

$2xy + 3 {y}^{2} = 13y \\ 2 \times 6 + 3 {y}^{2} = 13y \\ 3 {y}^{2} - 13y + 12 = 0 \\ 3 {y}^{2} - 9y - 4y + 12 = 0 \\ 3y(y - 3) - 4(y - 3) = 0 \\ (3y - 4)(y - 3) = 0 \\ 3y = 4 \: or \: y = 3 \\ y = \frac{4}{3} or \: y = 3$

3y = 4 or y = 3

y = 4/3 or y= 3