Question

How do you solve $y=4x-9$ and $y=x-3$ using substitution?

Answer 1

Hint: In this question, we have to find the value of x and y. Since it is given in the question that we have to solve using the substitution method. Therefore, we start solving this problem by substituting one equation in another equation and then solve for variables. First, we substitute equation $y=4x-9$ in equation $y=x-3$, and get a new equation in terms of x. Then, we subtract 9 on both sides of the equation and make the necessary calculations. After that, we will subtract x on both sides of the equation and then divide the equation by 3, to get a value of x. Then we will again substitute the value of x in the equation $y=4x-9$ , to get a value of y, which is our required answer.

Complete step by step answer:
According to the question, we have to find the value of x and y.
The equation given to us is $y=4x-9$ ---------- (1) and $y=x-3$ --------- (2)
Therefore, we use the substitution method.
Firstly, we will substitute equation (1) in equation (2), we get
$\Rightarrow 4x-9=x-3$
Now, we add 9 on both sides in the above equation, we get
$\Rightarrow 4x-9+9=x-3+9$
As we know, the same terms with opposite signs cancel out each other, we get
$\Rightarrow 4x=x-3+9$
On further simplification, we get
$\Rightarrow 4x=x+6$
Now, we will subtract x on both sides in the above equation, we get
$\Rightarrow 4x-x=x+6-x$
Now, in the RHS we see that there are the same variables with opposite signs, thus we will cancel out each other, we get
$\Rightarrow 4x-x=6$
On further solving, therefore we get
$\Rightarrow 3x=6$
Now, we will divide 3 on both sides in the above equation, we get
$\Rightarrow \dfrac{3}{3}x=\dfrac{6}{3}$
Therefore, we get
$\Rightarrow x=\dfrac{6}{3}$
On further simplification, we get
$\Rightarrow x=2$ --------- (3)
Now, we get the value of x, so we will substitute the value of equation (3) in equation (1), we get
$\Rightarrow y=4(2)-9$
Thus, on solving the brackets in the above equation, we get
$\Rightarrow y=8-9$
Therefore, we get
$\Rightarrow y=-1$
Therefore, for the equations $y=4x-9$ and $y=x-3$, we get the value of x and y as $2$ and $-1$ respectively.

Note:
Always make all calculations properly to avoid confusion and errors. One of the alternative methods to solve this problem is you can get both equations in terms of y, and then substitute one equation into another and make the calculations, to get the value of x and y, which is our required answer.