Question

How do you solve for y in $- 3y = 2x - 9$ ?

Answer 1

Here in this given equation is a linear equation. 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 RHS then solve the equation for y and on further simplification we get the required solution for the above equation.

Complete step-by-step solution:
The given equation is a linear equation. These equations are defined for lines in the coordinate system. An equation for a straight line is called a linear equation. The general representation of the straight-line equation is $y = mx + b$, it involves only a constant term and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, this equation is called a "linear equation of two variables," where y and x are the variables.
Consider the given equation
$\Rightarrow \,\,\,\, - 3y = 2x - 9$
Already the variable x and its coefficient in the RHS, so need to change. To solve y first multiply both side of equation by -1, then
$\Rightarrow \,\,\, - 1\,\left( { - 3y} \right) = - 1\left( {2x - 9} \right)$
On simplification we get
$\Rightarrow \,\,\,3y = - 2x + 9$
To solve the equation for y, divide 3 by both sides, then
$\Rightarrow \,\,\,\dfrac{{3y}}{3} = \dfrac{{ - 2x + 9}}{3}$
$\Rightarrow \,\,\,y = - \dfrac{2}{3}x + \dfrac{9}{3}$
$\Rightarrow \,\,\,y = - \dfrac{2}{3}x + 3$
Hence, the y value of the given linear equation $- 3y = 2x - 9$ is $y = - \dfrac{2}{3}x + 3$.

Note: The algebraic equation or an expression is a combination of variables and constants, it also contains the coefficient. The alphabets are known as variables. The x, y, z etc., are called as variables. The numerals are known as constants. The numeral of a variable is known as co-efficient. We have 3 types of algebraic expressions namely monomial expression, binomial expression and polynomial expression. By using the tables of multiplication, we can solve the equation.