Question

How do you rewrite this equation \[3x+5y=16\] solving for y?

Answer 1

Hint:In the given question we only assume ‘y’ as a variable and other given variable as constant. So, to solve this question we need to get ‘y’ on one side of the “equals” sign, and all the other numbers on the other side. To solve this equation for a given variable ‘y’, we have to undo the mathematical operations such as addition, subtraction, multiplication and division that have been done to the variables.

Complete step by step answer:
We have the given equation;
\[3x+5y=16\]
Subtract 3x from both the sides of the equation,
\[3x+5y-3x=16-3x\]
Simplify and combine like terms,
\[5y=16-3x\]
Divide both the sides of the equation by 5, we get
\[\dfrac{5y}{5}=\dfrac{16-3x}{5}\]
Simplifying the above, we get
\[ y=\dfrac{16}{5}-\dfrac{3x}{5}\]
Rewrite the equation in a standard form;
\[\therefore y=-\dfrac{3}{5}x+\dfrac{16}{5}\]

Therefore, \[y=-\dfrac{3}{5}x+\dfrac{16}{5}\] is the required solution.

Additional information:
In the given question, no mathematical formula is being used; only the mathematical operations such as addition, subtraction, multiplication and division is used.
-Use addition or subtraction properties of equality to gather variable terms on one side of the equation and constant on the other side of the equation.
-Use the multiplication or division properties of equality to form the coefficient of the variable term equivalent to 1.

Note:The important thing to recollect about any equation is that the ‘equals’ sign represents a balance. What the sign says is that what’s on the left-hand side is strictly an equal to what’s on the right-hand side. It is the type of question where only mathematical operations such as addition, subtraction, multiplication and division is used.