Find the point of intersection of the graphs of the function y = 4x-6 and y = -x + 4.

To find the intersection points of the graphs of the function given by the equations y = 4x – 6 and y = – x + 4, you need to solve a system of these equations.

System:

y = 4x – 6;

y = – x + 4.

We will solve the system by the substitution method. In the first equation, instead of y, we substitute the expression – x + 4. We get,

– x + 4 = 4x – 6;

y = – x + 4.

We solve the first equation of the system:

– x – 4x = – 6 – 4;

y = – x + 4.

System

– 5x = – 10;

y = – x + 4.

System:

x = 2;

y = – x + 4.

Substitute in the second equation x = 2.

System:

x = 2;

y = – 2 + 4 = 2.

Answer: (2; 2).