Without constructing, find the coordinates of the intersection of the graphs of the equation 5x-2y = 0 and x + 2y = 12

In order to find the coordinates of the intersection point of the graphs of the functions given by the equations 5x – 2y = 0 and x + 2y = 12 without performing the construction, we will solve the system of these equations.

System of equations:

5x – 2y = 0;

x + 2y = 12.

We solve the system using the substitution method.

System of equations:

5x – 2y = 0;

x = 12 – 2y.

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

System of equations:

5 (12 – 2y) – 2y = 0;

x = 12 – 2y.

We solve the first equation of the system:

5 * 12 – 5 * 2y – 2y = 0;

60 – 10y – 2y = 0;

-12y = -60;

y = -60: (-12);

y = 5.

System of equations:

x = 12 – 2y = 12 – 2 * 5 = 12 – 10 = 2;

y = 5.

Answer: (2; 5).