Question

How do you solve the system of equations $- 4x + 4y = 4$ and $y = 9x + 73$ ?

Answer 1

To solve the system of equations $- 4x + 4y = 4$ and $y = 9x + 73$ , at first, we will put the value $y$ from the second equation to the first equation. Then we will find the value of $x$ . Then we will put the value of $x$ in the second equation and get the value of $y$ .

Complete step by step answer:
We have the equations;
$- 4x + 4y = 4$ and
$y = 9x + 73$
We are numbering the equations as $1$ and $2$ respectively. Then it will be easy to mention the equation.
From the equation number $2$ we have;
$y = 9x + 73$
From the equation number $1$ we can easily cut out $4$ and we will get;
$- x + y = 1$
Let, give this equation number $3$ .
Now we will put this value $y$ in the equation number $3$ and we will get;
$- x + 9x + 73 = 1$
Now we will solve this equation and find the value of $x$ .
$\Rightarrow 8x + 73 = 1$
Subtracting $1$ from both side of the equation we will get;
$\Rightarrow 8x + 72 = 0$
Now subtracting $\;72$ from both side we will get;
$\Rightarrow 8x = - 72$
Dividing both side with $8$ we get;
$\Rightarrow x = \dfrac{{ - 72}}{8}$
After simplification we get;
$\Rightarrow x = - 9$
Now put this value of $x$ in equation number $1$ we get;
$y = 9( - 9) + 73$
After simplification we get;
$\Rightarrow y = - 81 + 73$
After addition we get;
$\Rightarrow y = - 8$
So the solution of the system of the equation is;
$x = - 9$
And $y = - 8$ .

Note:
This kind of system of equations of two variables can be easily solved by finding the value of one variable at first and then putting it to any of those equations. Then we will get the value of the second variable. The easy way to find the solution is to transform one equation’s coefficient of any one variable to another equation’s coefficient of that variable and then subtract one from another.
Alternative Method:
Given equations;
$- 4x + 4y = 4$ ……… $(1)$
And $y = 9x + 73$ ……….. $(2)$
From $(1)$ we get;
$- x + y = 1$ …….$(3)$
We can write $(3)$ as $y = 1 + x$ .
Now subtracting $(3)$ from $(2)$ we get;
$0 = 8x + 72$
Subtracting $\;72$ from both side;
$\Rightarrow 8x = - 72$
Dividing both side with $8$ we get;
$\Rightarrow x = \dfrac{{ - 72}}{8}$
After simplification we get;
$\Rightarrow x = - 9$
Put this value in $(2)$ we get;
$y = 9( - 9) + 73$
After simplification we get;
$\Rightarrow y = - 81 + 73$
After addition we get;
$\Rightarrow y = - 8$
So, the solution is;
$x = - 9$
And $y = - 8$ .