What is the equation of line whose slope  is -1/2 and passes through  the intersection of the lines x - y = -1 and 3x - 2y = 0?

Intersection point of the lines : $$x - y = -1$$ ------(i) and $$3x-2y=0$$ -------(ii)

Multiplying equation (i) by 2, => $$2x-2y=-2$$ -----(iii)

Subtracting equation (iii) from (ii), => $$x = 2$$

=> $$y = 2 + 1 = 3$$

Thus, line passes through (2,3)

Equation of line having slope $$m = \frac{-1}{2}$$ and passing through point $$(x_1,y_1)$$ is : $$(y-y_1)=m(x-x_1)$$

$$\therefore$$ Equation : $$(y-3)=\frac{-1}{2}(x-2)$$

=> $$2y-6=-x+2$$

=> $$x+2y=8$$

=> Ans - (A)