Find the coordinates of the intersection point of the graphs of the function y = 14-2.5x and y = 1.5x-18.

In order to find the intersection point of the straight lines given by the equations y = 14 – 2.5x and y = 1.5x – 18 without performing the construction, we solve the system of these equations.

System of equations:

y = 14 – 2.5x;

y = 1.5x – 18;

We solve the system using the substitution method.

System of equations:

1.5x – 18 = 14 – 2.5x;

y = 1.5x – 18;

We solve the first equation of the system:

1.5x + 2.5x = 14 + 18;

x (1.5 + 2.5) = 32;

4x = 32;

We are looking for an unknown factor:

x = 32: 4;

x = 8.

System of equations:

x = 8;

y = 1.5 * 8 – 18 = 12 – 18 = -6.

Answer: (8; -6).