Question

How do you solve for y in \[x + 5y = 25\]?

Answer 1

Hint: Here in this given equation is a linear equation with two variables. Here we have to solve for one variable. To solve this equation for y by using arithmetic operation we can shift the x variable to the right hand side of the equation then solve the equation for y and on further simplification we get the required solution for the above equation.

Complete step-by-step solution:
Given \[x + 5y = 25\].
Now we need to transpose the variable ‘x’ to the right hand side of the equation. So subtract ‘x’ on both sides of the equation.
\[
\Rightarrow x - x + 5y = 25 - x \\
\Rightarrow 5y = 25 - x \\
 \]
Now divide the whole equation by 5 we have
\[\Rightarrow \dfrac{{5y}}{5} = \dfrac{{(25 - x)}}{5}\]
\[\Rightarrow y = \dfrac{{(25 - x)}}{5}\]
Splitting the terms in the right hand side of the equation.
\[\Rightarrow y = \dfrac{{25}}{5} - \dfrac{x}{5}\]
\[y = 5 - \dfrac{x}{5}\] is the required solution.
If we observe the obtained solution we notice that it is in the form of the equation slope intercept form. That is \[y = mx + c\], where ‘m’ is slope and ‘c’ is y-intercept.
If we rearrange the obtained solution we have
\[y = - \dfrac{1}{5}x + 5\], where slope is \[ - \dfrac{1}{5}\] and the intercept is 5.

Note: By putting different values of x and then solving the equation, we can find the values of y. The algebraic equation or an expression is a combination of variables and constants, it also contains the coefficient. Generally we denote the variables with the alphabets. Here both ‘x’ and ‘y’ are variables. The numerals are known as constants and here 5. The numeral of a variable is known as co-efficient and here \[ - \dfrac{1}{5}\] is coefficient of ‘x’.