2. Every solution (x, y) of binary linear inequality (group) takes the coordinates of a point as the corresponding point on the plane, and the solution set of binary linear inequality (group) corresponds to a half plane (plane area) in the plane rectangular coordinate system.
3. The straight line L: ax+by+c = 0 (both A and B are not zero) divides the coordinate plane into two parts, one of which (half plane) corresponds to the binary linear inequality ax+by+c > 0 (or ≥0), and the other part corresponds to the binary linear inequality AX+BY+C.
4. Given the plane area, it is expressed by inequality (group). The method is: take any point outside all straight lines (such as the origin (0,0) of this question), substitute its coordinates into Ax+By+C, and judge whether it is positive or negative to determine the corresponding inequality.
5. The plane area represented by a binary linear inequality is a half plane divided by the corresponding straight line, which can be judged by substituting special points into the binary linear inequality test. When the straight line does not pass through the origin, the origin inspection is often selected, and when the straight line passes through the origin, (1, 0) or (0, 1) is often selected for substitution inspection. The plane region represented by binary linear inequalities is the plane region represented by its various inequalities. Delineation of lines and positioning of points.
6. The ordered number pair (x, y) consisting of the values of integers x and y satisfying the binary linear inequality (group) is called the solution of this binary linear inequality (group). All points corresponding to integer solutions are called integer points (also called lattice points), which are all in the plane region represented by this binary linear inequality (group).
7. When drawing the plane area represented by the binary linear inequality Ax+By+C≥0, the boundary should be drawn as a solid line, and the binary linear inequality AX+BY+C > 0, the boundary should be drawn as a dotted line.
8. if point P(x0, y0) and point P 1(x 1, y 1) are on the same side of the straight line l: ax+by+c = 0, then Ax0+By0+C and ax1+byl+c. If point P(x0, y0) and point P 1(x 1, y 1) are on both sides of the straight line L: ax+by+c = 0, then the signs of Ax0+By0+C and Ax 1+Byl+C are opposite.
9. The steps of abstracting binary linear inequalities (groups) from practical problems are:
(1) Set variables according to the meaning of the question;
(2) Analyze the variables in the problem, and list the inequalities between the constant and the variables X and Y according to various inequality relations;
(3) Combine inequalities with meaningful practical ranges of variables X and Y to form an inequality group.
The above are all the knowledge points in the first volume of senior three mathematics in Jiangsu Education Press: binary linear inequalities (groups) and simple linear programming problems. I hope it will help you review the knowledge points in this lesson!