Question

How do you solve for y in \[2x + 3y = 3\] ?

Answer 1

Hint: 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 answer:
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
 \[ \Rightarrow 2x + 3y = 3\]
We have to shift the variable x and its coefficient to the RHS, by add -2x on both sides, then
 \[ \Rightarrow 2x + 3y - 2x = 3 - 2x\]
On simplification we get
 \[ \Rightarrow 3y = 3 - 2x\]
To solve the equation for y, divide 3 by both sides, then
 \[ \Rightarrow \dfrac{{3y}}{3} = \dfrac{{3 - 2x}}{3}\]
 \[ \Rightarrow y = \dfrac{3}{3} - \dfrac{{2x}}{3}\]
 \[ \Rightarrow y = 1 - \dfrac{2}{3}x\]
Hence, the y value of the given linear equation \[2x + 3y = 3\] is \[\,y = 1 - \dfrac{2}{3}x\]
So, the correct answer is “ \[\,y = 1 - \dfrac{2}{3}x\] ”.

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.