Without constructing, find the coordinates of the intersection points of the graphs of the functions y = 23x

Without constructing, find the coordinates of the intersection points of the graphs of the functions y = 23x + 9 and y = 13x-21

In order to find the coordinates of the intersection points of straight lines without construction, which are given by the equations y = 23x + 9 and y = 13x – 21, we will solve a system of these equations.

System of equations:

y = 23x + 9;

y = 13x – 21.

Let us apply the substitution method to solve the system of equations. Let’s substitute in the first equation the expression from the second instead of the variable y.

System of equations:

13x – 21 = 23x + 9;

y = 13x – 21.

We solve the first equation of the system:

13x – 23x = 9 + 21;

-10x = 30;

x = -3.

System of equations:

x = -3;

y = 13 * (-3) – 21 = -39 – 21 = -60.

(-3; -60) intersection point of lines.