Answer:
x = [tex]-\frac{11}{5}, 3[/tex]
y = [tex]-\frac{8}{5},1[/tex]
Step-by-step explanation:
3xy - y² = 8 -------(1)
x - 2y = 1 ------(2)
From equation (2),
x = 2y + 1
By substituting the value of x in equation (1),
3y(2y + 1) - y² = 8
6y² + 3y - y² = 8
5y² + 3y - 8 = 0
5y² + 8y - 5y - 8 = 0
y(5y + 8) - 1(5y + 8) = 0
(y - 1)(5y + 8) = 0
y = [tex]-\frac{8}{5},1[/tex]
From equation (2),
x = 2y + 1
For y = [tex]-\frac{8}{5}[/tex],
x = [tex]-2(\frac{8}{5})+1[/tex]
x = [tex]-\frac{11}{5}[/tex]
For y = 1,
x = 2(1) + 1
x = 3
Therefore, x = [tex]-\frac{11}{5}, 3[/tex]
y = [tex]-\frac{8}{5},1[/tex]
