Which choice best describes the solution(s) for this system? −3x + 5y = −6 6x − 10y = 12 a) infinitely many solutions b) only one solution c) no solution d) the origin

The Equation of line have NO SOLUTION

Step-by-step explanation:

The Given equation of system as,

First line equation :

-3 x + 5 y = -6

Or, 5 y = 3 x - 6

Or,    y =

So , Slop of this line = m1 =

Again ,second line equation :

6 x - 10 y = 12

Or, 10 y = 6 x - 12

Or,   5 y = 3 x - 6

Or ,      y =  

So , Slop of this line = m2 =

∴      Slop of both the lines are equal , i.e m1 = m2 =

I.e both the lines do not intersect,and they are parallel to each other.

Hence, The Equation of line have NO SOLUTION