Calculate the coordinates of the intersection of two straight lines y = 4x + 2 and y = -x + 7.

To find the coordinates of the point of intersection of straight lines

y = 4x + 2;

y = -x + 7.

To solve the system, we use one of two possible methods – the substitution method.

Substituting -x + 7 in the first equation instead of y and we get the system:

-x + 7 = 4x + 2;

y = -x + 7.

Let’s now find the value of the variable x from the first equation:

-x + 7 = 4x + 2;

-x – 4x = 2 – 7;

x (-1 – 4) = -5;

-5x = -5;

x = -5: (-5);

x = 1.

System of equations:

x = 1;

y = -x + 7 = – (- 1) + 7 = 1 + 7 = 8.

The intersection point of the lines has coordinates (1; 8).