How do you solve y = x – 2 and y = 4x + 1?

Hint: We will first find two points which lie on y = x – 2 and then find two points lying on the line y = 4x + 1 and then plot them and see where they intersect and thus we have the required answer.

Complete step-by-step answer:
We are given the equations y = x – 2 and y = 4x + 1 which we are required to solve.
Now, let us take the first equation for once which is y = x – 2.
Here, if we put x = 0, we get y = -2 and if we put x = 2, we get y = 0.
So, we get a graph of this as follows:-

Now, we will consider the second equation which is y = 4x + 1.
If, we put x = 0, we get y = 1 and if we put x = 1, we get y = 5.

Now, we will plot them together in one graph and get the following picture:-

Here, the line in blue is y = x – 2 and the line in red is y = 4x + 1. Now, we can clearly see that they insect at the point (-1, -3).

Hence, the required answer is x = -1 and y = -3.

Note:
The students must note that there is an alternate and an easier way to do the same question. Let us do that as follows:-
We are required to solve y = x – 2 and y = 4x + 1.
Putting the value of y from the first equation in the second equation.
We will get:- x – 2 = 4x + 1
Taking x from addition in left hand side to subtraction in right hand side, we will get:-
$ \Rightarrow $ - 2 = 4x – x + 1
Simplifying the above equation and taking 1 from addition in right hand side to subtraction in left hand side, we will get:-
$ \Rightarrow $ - 2 – 1 = 3x
Simplifying and then dividing both sides by 3, we will then get:-
$ \Rightarrow $x = - 1.
Now, putting this in y = x – 2, we will get: y = -1 – 2 = -3. Thus we have the answer.