When you solve simultaneous equations you are looking for an exact value of x and y that satisfies both of the equations. Inequalities are different!

An equation with an inequality represents, not a line, but an area. y< 3x + 5 means the area below the line y = 3x + 5 (not including the line itself!).

So when you have two inequalities, y< 3x + 5 and y>= 2x - 7 you are looking for the area that is both below 3x + 5 and greater than 2x - 7 (because it includes the equal condition, this one *includes the line* 2x - 7!).

Because we are looking at areas, that means that a solution is not necessarily on either of the lines, it could be *anywhere inside* the area.

That makes graphical calculators like Desmos very attractive for solving problems with inequalities. Desmos shades the areas, making it easy to see whether a point lies inside or outside the area. Usually much faster!

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