Find three solutions to the linear equation 4x-2y = 3 so that the variables x and y have opposite signs.

Convert the original equation 4x-2y = 3 to express y through x:

4x – 3 = 2y;

y = 2x – 1.5.

The expression y = 2x – 1.5 is the equation of a straight line. Let’s calculate its points of intersection with the coordinate axes:

x = 0; y = – 1.5;

y = 0; x = 0.75.

The points of intersection with the coordinate axes (0; – 1.5) and (0.75; 0).

Since the coefficient in the equation of the straight line y = 2x – 1.5 at x is a positive number, and the points of intersection with the coordinate axes (0; – 1.5) and (0.75; 0), then, obviously, this straight line passes through the first , third and fourth quarter coordinates.

x and y are different only in the third quarter, i.e. at the points of the straight line between (0; – 1.5) and (0.75; 0).

Let’s select several solutions, choosing x from the interval (0; 0.75):

x1 = 0.1; y1 = – 1.3;

x2 = 0.2; y2 = – 1.1;

x3 = 0.3; y2 = – 0.9.

Answer: 0.1 and – 1.3; 0.2 and – 1.1; 0.3 and – 0.9.