Question

Solve for \[y\] in \[3x + 2y = 12\]

Answer 1

Hint: To solve for any variable in an equation, we isolate it to one side of the equation and the other terms to the other side of the equation. In this equation keep the term containing \[y\] to one side of the equation and all other terms to the other side and then simplify.

Complete step by step solution:
Given equation is \[3x + 2y = 12\].
Rewrite the equation as follows to bring the unknown term to be found to the left hand side of the equation:
\[2y = 12 - 3x\]
Divide each term by the coefficient of the unknown term to be found, in this case the coefficient of the unknown term \[y\] is \[2\], so divide both sides of the equation by \[2\]:
\[\dfrac{{2y}}{2} = \dfrac{{12}}{2} - \dfrac{{3x}}{2}\]
Cancel the common factor of \[b\]:
 \[y = 6 - \dfrac{{3x}}{2}\]
\[ \Rightarrow y = \dfrac{{12 - 3x}}{2}\]

Hence, \[y = \dfrac{{12 - 3x}}{2}\].

Note:
The value of \[y\] cannot be found out from only one equation as there are two variables involved in the equation. So to find the exact value of \[y\] at least two equations are needed. The two equations can be solved simultaneously to find the exact values of \[x\] and \[y\]. In this solution we have found \[y\] in terms of \[x\].