How do you solve the following linear system: 2x - 3y = 4 , 6y = 4x + 15 ?

Mar 17, 2017

The given pair of equations have no common solution.

Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 2 x - 3 y = 4$
[2]$\textcolor{w h i t e}{\text{XXX}} 6 y = 4 x + 15$

Convert [2] into standard form ($A x + B y = C$)
[3]$\textcolor{w h i t e}{\text{XXX}} 4 x - 6 y = - 15$

Notice that the Left Side of [3] is exactly $2$ times the Right Side of [1] (but the Right Side is not twice the Right Side of [1])
$\Rightarrow$ these equations represent parallel lines with no point(s) of intersection (i.e. no solution points)