Find the coordinates of the point of intersection of the straight line y = -5x + 14 with the straight line y = 6x-3.

In order to find the coordinates of the point of intersection of the straight lines, given by the equations y = -5x + 14 and y = 6x – 3, we must find a solution to the system of equations.

System of equations:

y = -5x + 14;

y = 6x – 3.

To solve the system of equations, we use the substitution method.

We substitute in the first equation instead of y the expression from the second and we get:

6x – 3 = -5x + 14;

y = 6x – 3.

We solve the resulting first equation of the system:

6x – 3 = -5x + 14;

6x + 5x = 14 + 3;

x (6 + 5) = 17;

11x = 17;

x = 17: 11;

x = 1 6/11.

System of equations:

x = 1 6/11;

y = 6 * 17/11 – 3 = 102/11 – 3 = 9 3/11 – 3 = 6 3/11.

(1 6/11; 6 3/11).