Question

How do you find a solution for y in $3x+y=-6$?

Answer 1

Hint: We start solving the problem by recalling the fact that solving for y from the given equation as to find the value of y such that only y is on the L.H.S (Left Hand Side) of the equation and all others on the R.H.S (Right Hand Side) of the equation. We then subtract $3x$ on both sides of the given equation and make the necessary calculations. We then take the common factor of all the terms present in the R.H.S (Right Hand Side) of the obtained equation to the required answer.

Complete step by step answer:
According to the problem, we are asked to solve for y in the function $3x+y=-6$.
We need to find the value of y as a function of combination of x and constant i.e., we need to find the value of y such that only y is on the L.H.S (Left Hand Side) of the equation and all others on the R.H.S (Right Hand Side) of the equation.
We have given $3x+y=-6$ ---(1).
Let us subtract both sides of equation (1) with $3x$.
$\Rightarrow 3x+y-3x=-6-3x$.
$\Rightarrow y=-6-3x$.
$\Rightarrow y=-3\left( x+2 \right)$.
We have found the value of y as $y=-3\left( x+2 \right)$.

$\therefore $ The solution for y in the function $3x+y=-6$ as $y=-3\left( x+2 \right)$.

Note: Whenever we get this type of problems, we should make sure that there is only the independent variable (in this problem y) present on the L.H.S (Left Hand Side) of the resultant equation. If we need to solve for x from the given equation, then we must finally get the answer resembling $x=f\left( y \right)$. Similarly, we can expect problems to solve for x in $4x-5y=10$.