Given:
[tex]4x-3y=-1[/tex]As it includes two variables x and y. The values of these variables is unknwon.
Moreover, to simplify the given equation for y.
To simplify the equation for y. We need to take y alone in one side of the equal to(=) sign.
For that we need to subtract 4x from both sides so that 4x -4x will be equal to 0 and we get y term alone.
[tex]\begin{gathered} 4x-3y=-1 \\ Subtract\text{ 4x from both sides} \\ 4x-4x-3y=-1-4x \end{gathered}[/tex]The term -4x is additive inverse of 4x.
[tex]\begin{gathered} -3y=-1-4x \\ \text{Divide by -3 on both sides} \\ -\frac{3y}{-3}=\frac{-1-4x}{-3} \\ y=-\frac{1}{-3}+(\frac{-4x}{-3})_{} \\ y=\frac{1}{3}+\frac{4x}{3} \end{gathered}[/tex]
