Question

How do you solve for y in the equation \[3x+y=12\]?

Answer 1

Hint: We are given an equation in two variables. We are asked to solve the equation for one variable. To do this we have to take the variable for which we want to solve to one side of the equation, and leave the other variable and constant terms to the other side of the equation. By this, we will get a relationship between the two variables. The coefficient of the variable for which we want to solve the equation should be one. We will do the same for the given two-variable equation.

Complete step-by-step solution:
We are given the equation \[3x+y=12\]. We are asked to solve it for y, to do this we have to take y to one side of the equation, leaving other variable and constant terms to the other side of the equation. The coefficient of they should be one on its side.
We can do this as follows,
Subtracting \[3x\] from both sides of the equation, we get
\[\Rightarrow 3x+y-3x=12-3x\]
\[\Rightarrow y=12-3x\]
The above equation gives the relationship between the two variables and satisfies the conditions. Hence, it is the solution.

Note: If we are given two equations in two variables, we can substitute this relationship in the other equation to find the solution values of the two variables that satisfies both of the given equations. Here we are given one equation, so we can only find the relationship between the variables.