Question

Graph the solution set of each system of inequalities. 2x + y \u003e 2 x - 3y \u003c 6

Accepted Answer

Step 1: Rewrite each inequality in slope-intercept form (y = mx + b) to make graphing easier. For the first inequality, start with $$4x + y \u003e 8. $$Subtract $$4x$$ from both sides to isolate $$y$$: $$y \u003e -4x + 8. $$Step 2: For the second inequality, $$6x - y  6x - 2. $$Step 3: Graph the boundary lines for each inequality. For $$y \u003e -4x + 8$$, graph the line $$y = -4x + 8. $$For $$y \u003e 6x - 2$$, graph the line $$y = 6x - 2. $$Use dashed lines because the inequalities are strict (greater than, not greater than or equal to). Step 4: Determine the solution region for each inequality by testing a point not on the line (commonly the origin (0,0) if it is not on the line). For $$y \u003e -4x + 8$$, check if (0,0) satisfies the inequality: $$0 \u003e -4(0) + 8$$ which is $$0 \u003e 8 ($$false), so shade the region opposite to where (0,0) lies. For $$y \u003e 6x - 2$$, check (0,0): $$0 \u003e 6(0) - 2$$ which is $$0 \u003e -2 ($$true), so shade the side containing (0,0). Step 5: The solution set to the system is the intersection of the shaded regions from both inequalities. Identify and shade the overlapping region on the graph, which represents all points satisfying both inequalities simultaneously.

Graph the solution set of each system of inequalities.
2x + y > 2
x - 3y < 6

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Graphing Linear Inequalities

System of Inequalities

Testing Points to Determine Shading

Graph the solution set of each system of inequalities. 2x + y > 2 x - 3y < 6