Question

How do you solve the equation for $ y $ : $ 4x - 2y = 6 $ ?

Answer 1

Hint: As we are given an equation with two variables and the degree of the equation is one, we can say that it is a linear equation in two variables. Since we know that, a pair of linear equations in two variables can be solved by various methods, here solving this single equation for $ y $ simply means finding the value of $ y $ in terms of $ x $ . We can do this by keeping $ y $ in LHS and everything else in RHS.

Complete step-by-step answer:
(i) We are given an equation:
 $ 4x - 2y = 6 $
As we can see, this is a linear equation in two variables as the degree of the equation is one and there are two variables present in the equation i.e., $ x $ and $ y $ .
In order to solve the given equation for $ y $ , we need to find the value of $ y $ in terms of $ x $ . Therefore, we will shift everything to RHS except for $ y $ .
So, as we have to remove $ 4x $ from LHS we will subtract it from LHS and to keep the equation balanced we will also subtract it from RHS. Therefore, subtracting $ 4x $ from both sides, we will get:
 $ 4x - 2y - 4x = 6 - 4x $
On simplifying it further, we get:
 $ - 2y = 6 - 4x $
(ii) Now, we are left with $ - 2y $ in LHS. Since we only want $ y $ in LHS, we will divide $ - 2y $ by $ - 2 $ in order to obtain $ y $ in LHS. To keep the equation balanced, we will also have to divide the RHS by $ - 2 $ . Therefore, dividing both the sides by $ - 2 $ , we will get:
 $ \dfrac{{ - 2y}}{{ - 2}} = \dfrac{{6 - 4x}}{{ - 2}} $
(iii) On simplifying, we will get:
 $
  y = \dfrac{6}{{ - 2}} - \dfrac{{4x}}{{ - 2}} \\
  y = - 3 + 2x \;
  $
Writing it in a standard form of $ y = mx + c $ , it will be:
 $ y = 2x - 3 $
Hence, solving $ 4x - 2y = 6 $ for $ y $ gives us $ y = 2x - 3 $
So, the correct answer is “ $ y = 2x - 3 $ ”.

Note: When we are asked to solve a linear equation in two variables, we must know it is an equation of a line and solving the equation for $ y $ means the same as writing the equation in the slope intercept form i.e., $ y = mx + c $ . The method will be the same to convert the equation into slope intercept form where $ m $ represents the slope of the line and $ c $ represents the $ y $ -intercept of the line. Here, since we got the equation as $ y = 2x - 3 $ , we can say that the slope of the line is $ 2 $ and the $ y $ -intercept is $ - 3 $ .