Calculate the coordinates of the intersection points of the graphs of the functions y = 3x-4 and y = 5x-10

To determine the coordinates of the intersection of the given graphs of functions, we equate the right sides of both functions, then solve the resulting equation.
We get: 3 * x – 4 = 5 * x – 10.
Subtract the variable 5 * x from both sides of the equation.

3 * x – 5 * x – 4 = 5 * x – 5 * x – 10.

-2 * x – 4 = -10.

Add 4 to both sides of the equation.

-2 * x – 4 + 4 = -10 + 4.

-2 * x = -6.

Multiply both sides of the equation by the number (-1).

-2 * x * (-1) = -6 * (-1).

2 * x = 6.

Divide both sides of the equation by 2.

2 * x / 2 = 6/2.

x = 3.

The first coordinate – point x was determined. Let’s find the second coordinate – y.

To do this, substitute the resulting value x into any of the equations: y = 3 * 3 – 4 = 9 – 4 = 5.

So, the intersection point of the graphs of the functions y = 3 * x – 4 and y = 5 * x – 10 has coordinates (3; 5).

Answer: the point of intersection of the given graphs of functions has coordinates (3; 5).