Question

What is the solution to the system of equations Y equals -1/4 X +2 and 3Y equals -3/4 X -6

Answer 1

`y \: = \: ( - 1)/(4) x \: + \: 2`

`3y \: = \: ( - 3)/(4) x \: - \: 6 \\ or \\ y \: = \: ( - 1)/(4) x \: - \: 2`

`y = y \\ ( - 1)/(4) x \: + \: 2 \: = \: ( - 1)/(4) x \: - \: 2 \\ or \\ 2 \: = \: - 2`
which is not possible,
Hence, the system has no solutions, as the lines are parallel and never intersect.

Answer 2

No solutions

Explanation:

y = -1/4 x+2

3y = -3/4 x -6

We can use substitution since the first equation is solved for y

Every time there is a y in the second equation, replace it with -1/4 x +2

3 (-1/4 x+2) = -3/4 x -6

Distribute

-3/4 x +6 = -3/4 x-6

Add 3/4 x to each side

-3/4 x + 3/4 x +6 = -3/4 x + 3/4x-6

6 = -6

Since this not a true statement, the system of equations has no solutions