Question

How do you solve for y in 2x = – 3y + 10?

Answer 1

Hint: We are given an equation as 2x = – 3y + 10. We are asked to solve for y. Solving for y means we are asked to rearrange the term in such a way that we can have a function given in the value of y. To do so we will use algebraic tools like addition, subtraction, multiplication, division. We also need the knowledge that we have to find the value of y in terms of x.

Complete step by step answer:
We are given the equation as 2x = – 3y + 10. We have to solve for y means from this equation we have to find the value of y. To do so we will rearrange it and we will shift the terms in such a way that we will get the y term separate and the other terms separate. To do in a simple way we will use the Mathematics Algebra tool which is addition, division, multiplication and subtraction.
Now, as we can see that we have 2x on the left side and on the right we have – 3y + 10 and we have to separate y from this. So, we will first remove the 10 from its side. So, we will subtract 10 from the left, as subtracting 10 only on one side will change the equation. So, we will subtract it from both sides. So, it won’t misbalance the equation. So, subtracting 10 on both the sides, we get,
\[2x-10=-3y+10-10\]
On simplifying, we get,
\[\Rightarrow 2x-10=-3y\]
Now as we can see that here we have – 3 with y, so we only need y. so, we will separate – 3 from y. To do so we will divide – 3 on both sides so that it will get separated as well as stay balanced. So, we get,
\[\Rightarrow \dfrac{2x-10}{-3}=\dfrac{-3y}{-3}\]
On simplifying, we get,
\[\Rightarrow y=\dfrac{-2x}{3}+\dfrac{10}{3}\]
As we know
\[\dfrac{a+b}{c}=\dfrac{a}{c}+\dfrac{b}{c}\]
Hence, we get,
\[\Rightarrow y=\dfrac{-2x+10}{3}\]

Note: Remember that we cannot subtract or add the constant to variable. We need to check and we only add or subtract like terms to like terms only. That is 2x + 3x = 5x, 3y + y = 4y or 2 + 3 = 5. We can never do 2 + 3y = 5y or 2 + 3x + 4y = 9yx. These are all wrong solutions.