Question

How do you solve for y $5x+6y-12=0$ ?

Answer 1

Hint: Now to solve the equation for y we will try to express y in terms of x. To do so we will simplify the equation by adding and subtracting terms on both sides of the equation till we have just y on LHS.

Complete step by step answer:
Now consider the given equation $5x+6y-12=0$ .
The given equation is a linear equation in two variables x and y. We know that the equation denotes a straight line in the XY plane.
Now to solve the equation for y we will write the equation in a form such that we express y in terms of x.
Now let us add 12 on both side of equation Hence we get,
$\begin{align}
  & \Rightarrow 5x+6y-12+12=12 \\
 & \Rightarrow 5x+6y=12 \\
\end{align}$
Now let us subtract 5x on both sides of the equation. Hence we get,
$\begin{align}
  & \Rightarrow 5x-5x+6y=12-5x \\
 & \Rightarrow 6y=12-5x \\
\end{align}$
Now we will divide the whole equation by the coefficient of y which in this case is 6. Hence we get,
$\begin{align}
  & \Rightarrow y=\dfrac{12}{6}-\dfrac{5}{6}x \\
 & \Rightarrow y=2-\dfrac{5}{6}x \\
\end{align}$
Hence we get the equation as y in terms of x.
Now if we substitute the values of x we will get the corresponding values of y.
For example if we substitute x = 0 we get y = 2, for x = 6 we get y = - 3.
Hence we have the solution for the equations.

Note:
Now note that here we can avoid adding and subtracting three terms on both sides of the equation. We can transpose the terms from one side to another instead. To do so we will shift the term from one side to another and change the sign of the term.