Question

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

Answer 1

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 = -6

Or, 5 y = 3 x - 6

Or,    y = $\frac{3}{5} x  - \frac{6}{4}$

So , Slop of this line = m1 = $\frac{3}{5}$

Again ,second line equation :

6 x - 10 y = 12

Or, 10 y = 6 x - 12

Or,   5 y = 3 x - 6

Or ,      y =  $\frac{3}{5} x - \frac{6}{5}$

So , Slop of this line = m2 = $\frac{3}{5}$

∴      Slop of both the lines are equal , i.e m1 = m2 = $\frac{3}{5}$

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

Hence, The Equation of line have NO SOLUTION

Answer 2

Answer:

A) infinitely many solutions

Step-by-step explanation:

I'm sorry i don't know how to break down the explanation but i know its right because I got it right on the test. :)