Question

How do you solve the following system $ 3x - 12y = 4,x - 4y = 3 $ ?

Answer 1

Hint: In order to determine the solution, rewrite the first equation by dividing both side of the equation with the number 3.We can clearly see that the system of equations is actually same as they are of the form $ x - 4y = \lambda $ . So for such a system of equations, no solution exists.

Complete step-by-step answer:
We are given pair of linear equation in two variables $ 3x - 12y = 4,x - 4y = 3 $
 $ 3x - 12y = 4 $
Rewriting the equation by dividing both sides of the equation with $ 3 $
\[\dfrac{1}{3}\left( {3x - 12y} \right) = 4\left( {\dfrac{1}{3}} \right)\]
\[x - 4y = \dfrac{4}{3}\]-----(1)
 $ x - 4y = 3 $ ----(2)
If we look at both the equations carefully, both the equations (1) and (2)are actually same as they have the form $ x - 4y = \lambda $
Since the system of equations are identical so no solution exists for such a system.
Therefore, the answer is that no solution exists for the given system of equations.

Note: Linear Equation in two variable: A linear equation is a equation which can be represented in the form of $ ax + by + c $ where $ x $ and $ y $ are the unknown variables and c is the number known where $ a \ne 0,b \ne 0 $.
The degree of the variable in the linear equation is of the order 1.
One must be careful while calculating the answer as calculation error may come.
Solution of two linear equations can be done by using elimination method, substitution method and cross multiplication method.