Find the coordinates of the intersection points of the graphs of the functions y = X / 2 and y = 3x-5

In order to find the coordinates of the intersection point of the graphs of the functions given by the equations y = x / 2 and y = 3x – 5 without performing the construction, we will solve the system of these equations.

System of equations:

y = x / 2;

y = 3x – 5.

We solve the system using the substitution method.

Let’s substitute in the first equation instead of y the expression from the second equation.

System of equations:

x / 2 = 3x – 5;

y = 3x – 5.

We solve the first equation of the system:

x / 2 = 3x – 5;

x = 6x – 10;

x – 6x = -10;

-5x = -10;

x = -10: (-5);

x = 2.

System of equations:

x = 2;

y = 3 * 2 – 5 = 6 – 5 = 1.

Answer: (2; 1).