Find the coordinates of the intersection of two straight lines 5 x + 2 y = 4 and 2 x + y = 1

We represent the equations of both lines with respect to y:

first line: y = (4 – 5x) / 2;

second straight line: y = 1 – 2x.

Let’s equate the right-hand sides of both equations:

(4 – 5x) / 2 = (1 – 2x); further (4 – 5x) = (2 – 4x), whence x = 2.

Substitute x = 2 in the equations of both lines:

y = (4 – 5 × 2) / 2 = -3; y = 1 – 2 × 2 = -3.

Thus, the lines intersect at a point with coordinates x = 2; y = -3.

Answer: x = 2; y = -3.