Question

How do you solve for $y$ in $- 3x + 5y = - 10$ ?

Answer 1

Hint: The equation that we need to solve here is a linear equation in two variables. But we need to solve this equation only for one variable. For that, we will simplify it by the way that we will keep the required variable terms on the left and the remaining terms on right and then simplify it further.

Complete step by step answer:
The given equation $- 3x + 5y = - 10$ , is a linear equation in two variables.
Here, we need to solve this equation for one variable only. So we simplify it further.
To solve it for $y$ , we add $3\;x$ on both sides, then we get
$- 3x + 5y + 3x = - 10 + 3x$
Because we know that positive and negative of the same term becomes zero.
$\Rightarrow 5y = - 10 + 3x$ ,
Now, to make the coefficient of $y$ , $1$ , we divide the above equation by $5$ on both sides,
$\Rightarrow \dfrac{{5y}}{5} = \dfrac{{ - 10 + 3x}}{5}$
$\Rightarrow y = \dfrac{{ - 10}}{5} + \dfrac{{3x}}{5}$ ,
Now the coefficient of $y$ becomes $1$ ,
$\Rightarrow y = - 2 + \dfrac{{3x}}{5}$ ,
$\Rightarrow y = \dfrac{{3x}}{5} - 2$ ,
This equation can also be written like this, as the commutative property for addition holds.

Hence, $y = \dfrac{{3x}}{5} - 2$ is the required solution of the given equation for $y$ .

Additional information:
The linear equation means that the degree of the equation is $1$ . In other words, we say that the highest power of the variables in the equation is $1$ . Thus we say that this is a linear equation. A linear equation represents a line.

Note: The representation of a linear equation in two variables is not unique. As $y = \dfrac{{3x}}{5} - 2$ , can be written as $y = - 2 + \dfrac{{3x}}{5}$ . Also, any pair of values of variables satisfying a given linear equation is known as its solution.