Find the point of intersection of the straight line x-y + 2 = 0 and the straight line passing through

Find the point of intersection of the straight line x-y + 2 = 0 and the straight line passing through the points M (-3; 1) and N (1; -3).

Let’s compose the equation of a straight line passing through two points M (-3; 1) and N (1; -3).

The equation of a straight line passing through two points has the form:

(y – y1) / (y2 – y1) = (x – x1) / (x2 – x1).

(y – 1) / (-3 – 1) = (x + 3) / (1 + 3).

(y – 1) / -4 = (x + 3) / 4.

y – 1 = – x – 3.

y = -x – 2.

Find the intersection points of the lines:

x – y + 2 = 0.

y = -x – 2.

x + 2 = -x – 2.

2 * x = -4.

x = -2.

y = 2 – 2 = 0.

Answer: The point of intersection of the lines has coordinates (-2; 0).