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?
Draw the graph for the linear equation given below:$$x + 3 = 0$$
$$x + 3 = 0 => x = -3 $$
In the linear equation $$ x = - 3 $$, there is no term for $$ y $$. This means, that $$y$$ can take any value.
Points lying on the line $$ x =- 3 $$ can be $$ (-3,2), (-3, 0) $$ or $$ (-3, -1) $$. Plotting these points on the graph paper and joining them, we get the graph for $$ x = -3 $$.
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?
$$9x+3y+12=0\\18x+6y+24=0$$
The lines representing the linear equations $$2x - y - 3$$ and $$4x - y = 5$$
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