Question

How do you solve for y in \[3x - 2y = 10\]?

Answer 1

Hint: Here in this question, we have to find the equation for only the term that is y. The equation involves two variables x and y, by shifting the terms or by using the arithmetic operations to equation we have to find the equation for the y. Hence we get the equation.

Complete step-by-step answer:
The given equation or expression is an algebraic expression, where it is a combination of both variables and constants where variables are alphabets and the constants are numbers. The given equation is a binomial equation. The binomial equation is an algebraic equation which contains two terms and the arithmetic operations that are addition and subtraction.
Now consider the given equation.
 \[3x - 2y = 10\]
Now subtract 3x on both sides
 \[ \Rightarrow 3x - 2y - 3x = 10 - 3x\]
In the LHS of the equation the term 3x will gets cancels so we have
 \[ \Rightarrow - 2y = 10 - 3x\]
The LHS of the above equation is having the negative sign, so we multiply the entire equation by -1. On multiplying with -1 we have
 \[ \Rightarrow 2y = 3x - 10\]
The above equation in the LHS we have 2y, but need the equation for y. so we divide the above equation by 2 we get
 \[ \Rightarrow y = 5 - \dfrac{3}{2}x\]
Hence, we have solved for y and hence we have determined the equation for y.
So, the correct answer is “$ y = 5 - \dfrac{3}{2}x$”.

Note: The equation can be solved for both x and y. To write the equation in the form x and y we use simple arithmetic operations. While shifting or transforming the number from LHS to RHS the sign of the term will change so we should take care of the sign. Otherwise we can cancel the term by using the arithmetic operations.