Question

How do you solve $ 2x - 6y = 6 $ and $ - 4x + 12y = - 18 $ ?

Answer 1

Hint: Here we are given two sets of equations and there are two variables in it. So, we will use elimination method to find out the required values for the unknowns.

Complete step-by-step answer:
Take the given expressions:
 $ - 4x + 12y = - 18 $
Take common multiple common from the above equation from both the sides of the equation
 $ - 2x + 6y = - 9 $ …. (A)
 $ 2x - 6y = 6 $ ….. (B)
Add equations (A) and (B), where the left hand side of equation (A) is added to the left hand side of equation (B) and similarly for the right hand side of the equation.
\[( - 2x + 6y) + (2x - 6y) = ( - 9) + 6\]
When there is a positive sign outside the bracket then the sign of the terms remains the same.
\[ - 2x + 6y + 2x - 6y = ( - 9) + 6\]
Make the like terms together.
 $ \underline { - 2x + 2x} + \underline {6y - 6y} = - 3 $
Like terms with equal values and opposite signs cancels each other. Also, when you subtract a bigger number from the smaller number you have to give a sign of the bigger number to the resultant value.
 $ \Rightarrow 0 = - 3 $
The above expression is not possible, so the solution of the given set of equations does 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 do not change and remain the same and if there is negative sign outside the bracket then all the terms inside the bracket changes. Positive terms change to the negative and the negative term changes to the positive.