Question

Solve the simultaneous equation

Answer 1

Answer:

x = $-\frac{11}{5}, 3$

y = $-\frac{8}{5},1$

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 = $-\frac{8}{5},1$

From equation (2),

x = 2y + 1

For y = $-\frac{8}{5}$,

x = $-2(\frac{8}{5})+1$

x = $-\frac{11}{5}$

For y = 1,

x = 2(1) + 1

x = 3

Therefore, x = $-\frac{11}{5}, 3$

                  y = $-\frac{8}{5},1$