Question

y=1/2x-3/2 or 2y-x+3=0,​

Answer 1

Given ,

$\bold {\: \: \: • \: y \: = \frac{1}{2x} - \frac{3}{2} } \: \: - - - (1)$

$\bold {\: \: \: • \: 2y - x + 3\: = 0 } \: \: - - - (2)$

To find :—

• Value of x and y

Putting the value of y in eq(2) , we have

$\: \: \: \bold{2 \times (\frac{1}{2x} - \frac{3}{2} ) - x + 3 = 0}$

$\implies \: \: \: \bold{2 \times ( \frac{2 - 6x}{4x} ) - x + 3 = 0}$

$\implies \: \: \: \bold{2 \times 2 \times ( \frac{1 - 3x}{4x} ) - x + 3 = 0}$

$\implies \: \: \: \bold{ ( \frac{1 - 3x}{x} ) - x + 3 = 0}$

$\implies \: \: \: \bold{ \frac{1 - 3x - {x}^{2} + 3x }{x} =0 }$

$\implies \: \: \: \bold{ \frac{1 - {x}^{2} }{x} = 0}$

$\implies \: \: \: \bold{1 - {x}^{2} } = 0$

$\implies \: \: \: \bold {{x}^{2} = 1}$

$\implies \: \: \: \bold {{x}^{} = \sqrt{1} }$

$\implies \: \: \: \boxed{\bold {{x}^{} = ±{1} }}$

* If x = 1, then

~ 2y - 1 + 3 = 0 { from eq(2)}

→ 2y + 2 = 0

→ 2y = -2

→ y = -2/2

→ $\boxed{\bold{y\:=-1}}$

* If x = -1 , then

~ 2y - (-1) + 3 = 0

→ 2y + 1 + 3 = 0

→ 2y + 4 = 0

→ 2y = -4

→ y = -4/2

→ $\boxed{\bold{y\:=-2}}$

★ So, the value of x and y are 1 , -1 and -1 , 2 respectively .