Without graphing answer the questions for the following line

Without graphing, answer the questions for the following linear system x + 2y = 0 12y = -6x Is the system inconsistent, or are the equations dependent, or neither? Is the graph a pair of intersecting lines, a pair of parallel lines, or one line? Does the system have one solution, no solution or an infinite number of solutions? Is the system inconsistent, or are the equations dependent, or neither? Inconsistent system Dependent equations

Solution

x+2y =0

12y = -6x

Rewriting the second equation

12y +6x =0

\'divide by 6 : 2y +x =0

so both given equations are same i.e. one equation.

So, the equations are neither inconsistent nor dependent

Graph is just one line.

There are infinte solution to this equation.