Question

How do you solve for $ y:4x - 3y = 12? $

Answer 1

Hint: Here we will take the given equation and as per the required term will frame the equation in it. Also we will use the standard mathematical simplification method to get the value for “y”.

Complete step-by-step answer:
Take the given expression –
 $ 4x - 3y = 12 $
The above expression can be re-written as –
 $ 12 = 4x - 3y $
Now, take the term with “y” on the left hand side of the equation and the constant on the right from the left. Remember when you move any term from one side to another, then the sign of the terms are also changed. Positive terms become negative and vice-versa.
 $ 3y = 4x - 12 $
When the term multiplicative on one side is moved to the opposite side then it goes to the denominator of the equation.
 $ \Rightarrow y = \dfrac{{4x - 12}}{3} $
When you have a common denominator then we can split the numerator and can give individual or separate denominators to each of the numerators.
 $ \Rightarrow y = \dfrac{{4x}}{3} - \dfrac{{12}}{3} $
Find the factors on the right hand side of the equation of the second term.
 $ \Rightarrow y = \dfrac{{4x}}{3} - \dfrac{{4 \times 3}}{3} $
Common multiples from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
 $ \Rightarrow y = \dfrac{{4x}}{3} - 4 $
This is the required solution.
So, the correct answer is “ $ y = \dfrac{{4x}}{3} - 4 $ ”.

Note: Be careful while moving any terms from one side to another. When the side of the term is changed then the sign of the term is also changed. Positive term becomes negative and negative term becomes positive.
While doing simplification remember the golden rules-
I.Addition of two positive terms gives the positive term
II.Addition of one negative and positive term, you have to do subtraction and give sign of bigger numbers, whether positive or negative.
III.Addition of two negative numbers gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.