Question

How do you solve the system of equations $ - 5x + y = 18$ and $5x + 5y = - 30$?

Answer 1

Hint: We will just add the two equations $ - 5x + y = 18$ and $5x + 5y = - 30$. Then, we will just obtain the equation in y and thus we can get the value of y and x as well.

Complete step by step solution:
We are given that we are required to solve the system of equations $ - 5x + y = 18$ and $5x + 5y = - 30$.
Let us assume that $ - 5x + y = 18$ is equation number 1 and $5x + 5y = - 30$ as equation number 2.
Now, we will just add both the equation number 1 and 2, we will then obtain the following expression with us:-
$ \Rightarrow \left( { - 5x + y} \right) + \left( {5x + 5y} \right) = 18 + \left( { - 30} \right)$
Simplifying the brackets on the left hand side and the right hand side, we will then obtain the following equation with us:-
$ \Rightarrow - 5x + y + 5x + 5y = 18 - 30$
Simplifying the right hand side calculations’ on the right hand side and clubbing the terms with x on the left hand side, we will then obtain the following equation with us:-
$ \Rightarrow y + 5y = - 12$
Simplifying the left hand side by clubbing the terms with y on the left hand side, we will then obtain the following equation with us:-
$ \Rightarrow 6y = - 12$
Dividing both sides of the above equation by 6, we will then obtain the following equation with us:-
$ \Rightarrow y = - 2$
Putting this in equation number 1, we will then obtain the following equation with us:-
$ \Rightarrow - 5x + ( - 2) = 18$
Simplifying the left hand side, we will then obtain the following equation:-
$ \Rightarrow - 5x - 2 = 18$
Taking all the constant on the right hand side and clubbing them, we will then obtain the following equation:-
$ \Rightarrow - 5x = 20$
Simplifying it further, we will obtain:-
$ \Rightarrow x = - 4$

Thus, the answer is x = - 4 and y = - 2.

Note:-
The students must note that we have an alternate way to do the same question.
We are given that we are required to solve the system of equations $ - 5x + y = 18$ and $5x + 5y = - 30$.
Let us assume that $ - 5x + y = 18$ is equation number 1 and $5x + 5y = - 30$ as equation number 2.
We can write equation 1 as $y = 18 + 5x$.
Putting this in equation number 2, we will then obtain the following equation:-
$ \Rightarrow 5x + 5\left( {18 + 5x} \right) = - 30$
Simplifying it, we obtain:-
$ \Rightarrow 30x + 90 = - 30$
Simplifying it further, we will then obtain:-
$ \Rightarrow x = - 4$
Thus, we have the required answer.