Question

Solve for \[y\] in \[ax + by = c\].

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.

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

Additional information:
In equations like the above equation it is considered that \[a,b,c\] are constants and \[x,y\] are variables. For example \[5x + 2y = 7\], this is an equation of the above form where \[a = 5\], \[b = 2\], \[c = 7\]. Hence here \[y = \dfrac{{7 - 5x}}{2}\]. For solving these equations we require two equations as there are two variables.

Note: If mentioned in the question then the unit of the unknown variable should be mentioned along with the numerical coefficient of the variable in the answer. Units of all the variables should be in the same system of units in an equation. The unit of \[y\] depends on the unit of the variable \[x\].