Question

How do you solve $ 3y + 3 = 6x $ and $ 2y - 4x = 6 $ ?

Answer 1

Hint: Here we are given two sets of equations, first of all we will convert the coefficient of any of the variables common in both the set of equations. Then will use the elimination method to get the values of x and y.

Complete step by step solution:
Take the given expressions:
 $ 3y + 3 = 6x $
Move variables on one side of the equation. When you move any term from one side to another then the sign of the terms also changes. Positive terms become negative and vice versa.
 $ 6x - 3y = 3 $
Take out the common factor from all the given terms.
 $ 2x - y = 1 $
Multiply the above expression by
 $ 4x - 2y = 2 $ …. (A)
 $ 2y - 4x = 6 $ ….. (B)
Add equations (A) and (B)
Add the left hand side of both the equations and right hand side of the equations.
 $ 4x - 2y + 2y - 4x = 6 + 2 $
Like values with the same value and opposite sign cancels each other.
 $ \Rightarrow 0 = 8 $
The above relation is not possible.
Hence, the solutions for the given set of equations do not exist.

Note: Always remember that when we expand the brackets or open the brackets, the sign outside the bracket is most important. If there is a positive sign outside the bracket then the values inside the bracket does not change and if there is a negative sign outside the bracket then all the terms inside the bracket changes. Positive terms change to negative and negative term changes to positive.