Find the coordinates of the intersection of the lines 5x-2y-3 = 0 and -2x + y + 1 = 0

1) First, we express in each equation the variable y in terms of x.

a) 5x – 2y – 3 = 0;

– 2y = 3 – 5x;

y = (3 – 5x) / (- 2);

y = (5x – 3) / 2.

b) – 2x + y + 1 = 0;

y = 2x – 1.

2) Equate the right-hand sides of the resulting equations, solving the resulting equation, find the abscissa of the intersection point, i.e. coordinate x.

(5x – 3) / 2 = 2x – 1 – multiply both sides of the equation by 2;

2 (5x – 3) / 2 = 2 (2x – 1) – reduce the fraction on the left side of the equation by 2; on the right side of the equation, open the bracket by multiplying 2 by each term in the bracket, by 2x and by (- 1);

5x – 3 = 4x – 2;

5x – 4x = – 2 + 3;

x = 1.

3) Find the ordinate of the intersection point of the graphs.

y = 2x – 1 = 2 * 1 – 1 = 2 – 1 = 1.

Answer. (eleven).