Question

How do you solve for y in $3x = 2y - 18$ ?

Answer 1

Hint: We know that we need the “n” number of equations to find the value of “n” unknown variables. In the given algebraic expression, we have only one equation but 2 unknown quantities. As the unknown quantities are variable, we can get different values of one variable on putting different values of the other variable, that is, we can express one variable in terms of the other variable. In this question, we have to solve for y so we will express y in terms of x. For that, we will rearrange the equation such that y lies on the one side of the equation and all other terms lie on the other side.

Complete step-by-step solution:
We are given that $3x = 2y - 18$
To solve for the value of y, we take 18 and 2 to the left-hand side –
$
  3x + 18 = 2y \\
   \Rightarrow y = \dfrac{1}{2}(3x + 18) \\
   \Rightarrow y = \dfrac{3}{2}x + 9 \\
 $
Hence, when $3x = 2y - 18$ , we get $y = \dfrac{3}{2}x + 9$

Note:In this question, we are given an algebraic expression containing two unknown variable quantities. The mathematical equations that are a combination of numerical values and alphabets are known as algebraic expressions. The alphabets and numerical values are linked via arithmetic operations like addition, subtraction, multiplication and division, and the alphabets represent some unknown quantities. We have obtained an expression in which y lies on one side and the other side contains x and some constant terms. Thus by putting different values of x and then solving the equation, we can find the values of y.