Q:

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

Accepted Solution

A:
Answer:The Equation of line have NO SOLUTION Step-by-step explanation:The Given equation of system as,First line equation :-3 x + 5 y = -6Or, 5 y = 3 x - 6Or,    y = [tex]\frac{3}{5} x  - \frac{6}{4}[/tex] So , Slop of this line = m1 = [tex]\frac{3}{5}[/tex]Again ,second line equation :6 x - 10 y = 12 Or, 10 y = 6 x - 12Or,   5 y = 3 x - 6Or ,      y =  [tex]\frac{3}{5} x - \frac{6}{5}[/tex] So , Slop of this line = m2 = [tex]\frac{3}{5}[/tex]∴      Slop of both the lines are equal , i.e m1 = m2 = [tex]\frac{3}{5}[/tex]I.e both the lines do not intersect,and they are parallel to each other. Hence, The Equation of line have NO SOLUTION