Question

Determine of the following equation is linear if the equation is linear convert it standard form AX + BY =C

Answer 1

Solution:

Given:

$(-6+y)^2-y^2=-5x+6$

Simplifying the equation further to confirm if it is linear or not.

$\begin{gathered} (-6+y)^2-y^2=-5x+6 \\ (-6+y)(-6+y)-y^2=-5x+6 \\ 36-6y-6y+y^2-y^2=-5x+6 \\ 36-12y=-5x+6 \\ Since\text{ no power exceeds one, then it is linear.} \end{gathered}$

Rewriting the equation in standard form;

$\begin{gathered} 36-12y=-5x+6 \\ 5x-12y=6-36 \\ 5x-12y=-30 \end{gathered}$

Therefore, it is linear.

The equation in standard form is;

5x - 12y = -30