Find the coordinates of the intersection point of the graphs of the functions y = x + 2 and y = 4x-1.

To find the coordinates of the point of intersection of the straight lines given by the equations y = x + 2 and y = 4x – 1, you need to solve a system consisting of these equations:

y = x + 2;

y = 4x – 1.

We solve the system using the substitution method:

In the second equation, instead of y, substitute x + 2 and solve the resulting equation for the variable x:

y = x + 2;

x + 2 = 4x – 1.

System:

y = x + 2;

3x = 3.

System:

y = x + 2;

x = 1.

Let us recall the first equation of the system. Substitute the value x = 1 into it and find the value of y:

y = 1 + 2 = 3;

x = 1.

Answer: (1; 3) – the point of intersection of the lines.