Question

How do you solve $5x + 6y = 3x + 2$ ?

Answer 1

To solve such questions first bring all the terms with coefficient $x$ to one side of the equation. Then simplify the equation further divide that equation by a number $2$ . Further simplifying we get the required solution for the given equation.

Complete step by step answer: Given the equation $5x + 6y = 3x + 2$
Here it is asked to find the solution to the given equation.
Consider the given equation, that is,
$5x + 6y = 3x + 2$
Next, take $5\;x$ to the right-hand side of the equation. That is, $6y = 3x + 2 - 5x$
Simplifying further the above equation we get,
$6y = - 2x + 2$
Next divide both the LHS and RHS of the equation with the number $2$ , that is
$\dfrac{{6y}}{2} = \dfrac{{ - 2x}}{2} + \dfrac{2}{2}$
Simplifying further we get,
$3y = - x + 1$
Rearranging the terms we get
$3y = 1 - x$
Hence the solution of the equation $5x + 6y = 3x + 2$ is $3y = 1 - x$ .

Additional information:
A variable can be defined as a quantity that is not fixed. An algebraic expression can be made up of variables, constants, and operators. An equation can be defined as one which allows only a specific value of a variable. For a given term to be an equation, the left-hand side should be equal to the right-hand side. If they are not equal then it cannot be an equation. The value of the variable, which we get by solving the equation, is known as the solution of the equation.

Note:
These types of questions are easy to solve. The only mistake one can make is while doing subtraction or while dividing. Always start by taking the terms on the left-hand side with coefficient $x$ to the right-hand side and then by simplifying it.