Find the abscissa of the intersection point of the graphs of the function y = 7x and y = 8x-5

Find the abscissa of the point of intersection of the graphs of the function given by the equations y = 7x and y = 8x – 5.

The intersection abscissa is the x-coordinate value of the intersection point of the function graphs.

To find it, we solve the system of equations:

y = 7x;

y = 8x – 5.

We will solve the system by the substitution method.

Let us substitute in the first equation of the system instead of the variable y the expression 8x – 5 (from the second equation).

System:

8x – 5 = 7x;

y = 7x.

We solve the resulting first equation of the system:

8x – 7x = 5;

x (8 – 7) = 5;

x = 5.

Answer: x = 5 abscissa of the intersection point of the graphs of the function