Question

How do you solve the system of equations 4x + 3y = - 19 and 7x + 27 = y ?

Answer 1

Hint: We will find the value of y from the second equation and then put it in the first equation. After that we will get the value of x and then put that in second equation to get the value of y.

Complete step by step solution:
We are given that we are required to solve the system of equations 4x + 3y = - 19 and 7x + 27 = y.
We will use substitution to solve the same.
Let us terms the given equation 4x + 3y = - 19 as the equation number 1 and the given equation 7x + 27 = y as equation number 2.
Putting the value of y from equation 2 in equation number 1, we will then obtain the following expression with us:-
$ \Rightarrow $4x + 3 (7x + 27) = - 19
Simplifying the left hand side of the above expression, we will then obtain the following equation:-
$ \Rightarrow $4x + 21 x + 81 = - 19
Simplifying the left hand side of the above expression further, we will then obtain the following equation:-
$ \Rightarrow $25x + 81 = - 19
Taking 81 from addition in the left hand side of the above expression to subtraction in the right hand side, we will then obtain the following expression:-
$ \Rightarrow $25x = - 100
Simplifying this further, we will then obtain the following equation:-
$ \Rightarrow $x = - 4
Thus, we get: x = - 4
Putting this in equation number 2, we will then obtain the following equation:-
$ \Rightarrow $y = 7 (- 4) + 27
Simplifying the calculations, we will then obtain the following equation:-
$ \Rightarrow $y = - 28 + 27 = - 1

Hence, the answer is x = - 4 and y = - 1.

Note: The students must note that you may use alternate methods for solving the equations other than using the substitution method.
Alternate Way:
We are given that we are required to solve 4x + 3y = - 19 …………(1) and 7x + 27 – y = 0 ………(2)
Multiplying the equation 2 by 3, we have: 21x + 81 – 3y = 0 …………(3)
Adding the equation number 1 and equation number 3, we will then obtain the following equation:-
$ \Rightarrow ${4x + 3y} + {21x + 81 – 3y} = - 19
Simplifying the equation, we will then obtain the following equation:-
$ \Rightarrow $25x = - 100
Thus, we have x = - 4
Therefore, by putting this in equation number 2, we get y = - 1.
Hence, the answer is x = - 4 and y = - 1.