Find the coordinates of the intersection point of the graphs of the linear function y = -2x + 3 and y = 2x-5.

In order to find the coordinates of the point of intersection of the lines y = -2x + 3 and y = 2x – 5, which are given by the equations, without performing the construction, we will solve the system of these equations.

System of equations:

y = -2x + 3;

y = 2x – 5.

We will solve the system using the substitution method. Substitute the expression 2x – 5 in the first equation for y.

System of equations:

2x – 5 = -2x + 3;

y = 2x – 5.

We solve the first equation of the system and get:

2x + 2x = 3 + 5;

4x = 8;

x = 8: 4;

x = 2.

System of equations:

x = 2;

y = 2x – 5 = 2 * 2 – 5 = 4 – 5 = -1.

Answer: (2; -1).