Question

Solve for x and y simultaneously:
y-2x=3 and (x-y)(x+2y)= -18

Answer 1

Step-by-step explanation:

$y - 2x = 3 \: \: - - - - 1 \\ \\ (x - y)(x + 2y) = - 18 \\ \\ x(x + 2y) - y(x + 2y) = - 18 \\ \\ {x}^{2} + 2xy - xy - 2 {y}^{2} \\ \\ {x}^{2} + xy - 2 {y}^{2} \\ \\ from1 \\ \\ y - 2x = 3 \\ \\ y =3 + 2x \\ \\ substituting \: y = 3 + 2x \\ \\ {x}^{2} + xy - 2 {y}^{2} \\ \\ {x}^{2} + x(3+ 2x) - 2 ({3 + 2x}^{2} ) \\ \\ {x}^{2} + 3x + 2 {x}^{2} - 6 - 4 {x}^{2} \\ \\ - {x}^{2} + 3x - 6 \\ \\ - {x}^{2} + 2x + 3x - 6 \\ \\ - x(x + 2) + 3(x + 2) \\ \\ x + 2 = 0 \: \: - x + 3 = 0 \\ \\ x = - 2 \\ \\ x = 3 \\ \\ putting \: x = 3 \\ \\ we \: get \: the \: vale \: of \: y$