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

A) infinitely many solutions

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. :)

Answer 2

The Equation of line have NO SOLUTION

Explanation:

The Given equation of system as,

First line equation :

-3 x + 5 y = -6

Or, 5 y = 3 x - 6

Or, y =
`(3)/(5) x  - (6)/(4)`

So , Slop of this line = m1 =
`(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 =
`(3)/(5) x - (6)/(5)`

So , Slop of this line = m2 =
`(3)/(5)`

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