Physical World
The paths traced by the wheels of two trains are given by equations $$x + 2y - 4 = 0$$ and $$2x + 4y - 12 = 0$$. Will the paths cross each other?
The lines representing the linear equations $$2x - y - 3$$ and $$4x - y = 5$$
The given lines are
$$2x - y = 3$$
Here $$a_{1} = 2, b_{1} = -1, c_{1} = 3$$
and $$4x - y = 5$$
Here $$a_{2} = 4, b_{2} = -1, c_{2} = 5$$
$$\therefore \dfrac{a_1}{a_2} = \dfrac{2}{4} = \dfrac{1}{2}$$ and $$\dfrac{b_1}{b_2} = 1$$
$$\because \dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$$
Thus, lines will intersect at a point. Hence the correct option is (A).
The paths traced by the wheels of two trains are given by equations $$x + 2y - 4 = 0$$ and $$2x + 4y - 12 = 0$$. Will the paths cross each other?
Draw the graph for the linear equation given below:$$x + 3 = 0$$
$$9x+3y+12=0\\18x+6y+24=0$$
If the pair of linear equation in two variable has infinite number of solutions, then the lines represented by these equation are:
The value of $$\lambda$$ for which $$x + 2y + 7 = 0$$ and $$2x + \lambda y + 14 = 0$$ represent coincident lines is