Two lines intersect at point C. Calculate the coordinates of point C. 2x-3y = 5 x + 2y = -8

Given two equations of straight lines, it is necessary to find the point C of their intersection. To do this, you need to solve a system of two equations.

2 x – 3y = 5.

X + 2y = – 8.

Let’s transform the equations. Let’s select in the first y, and in the second equation x.

3y = 2x – 5.

x = – 8 – 2y.

Substitute the x value into the first equation.

3y = 2 (-8 – 2y) -5 = -16 – 4y – 5 = -4y – 21.

From here we find y.

y = -3. Now knowing y, we find the value of x.

x = -8 – 2 (-3) = -8 + 6 = -2.

The coordinates of the point of these lines are C (-2, -3).