jessgomez1325
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Graph the solution to the following system of inequalities.
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HallsofIvy
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Do you know what "graph \(\displaystyle y\le 3x+ 8\)" means?
HallsofIvy
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First do you understand what it means to "graph" an equation or inequality in variables x and y? It means to mark, in some way, those (x, y) points on an xy-plane that satisfy the equation or inequality.
Do you understand that the graph of "y= 3x+ 8" is a straight line in the xy-plane? If x= 0 then y= 3(0)+ 8= 0+ 8= 8 so (0, 8) is a point on that line. If x= 5, y= 3(5)+ 8= 15+ 8= 23 so (5, 23) is a point on that line. Since two points determine a line, mark (0, 8) and (5, 23) on you graph then draw the line through those two points.
The line "y= 3x+ 8" separates "y< 3x+ 8" from "y> 3x+ 8". The graph of "\(\displaystyle y\le 3x+ 8\)" is that line and the region below it. Mark that region by drawing, say, horizontal lines through it.
Similarly, if x= 0, y= -2(0)+3= 0+ 3= 3 and if x= 5, y= -2(5)+ 3= -10+ 3= -7 so (0, 3) and (5, -7) are points on the line y= -2x+ 3.
The line "y= -2x+ 3" separates "y< -2x+ 3" from "y> -2x+ 3". The graph or "\(\displaystyle y\ge -2x+ 3\)" is that line and the region above it. Mark that region by drawing, say, vertical lines through it.
The region in which both inequalities are true, the "solution to the system of inequalities" is the region that has both horizontal and vertical lines.
Do you understand that the graph of "y= 3x+ 8" is a straight line in the xy-plane? If x= 0 then y= 3(0)+ 8= 0+ 8= 8 so (0, 8) is a point on that line. If x= 5, y= 3(5)+ 8= 15+ 8= 23 so (5, 23) is a point on that line. Since two points determine a line, mark (0, 8) and (5, 23) on you graph then draw the line through those two points.
The line "y= 3x+ 8" separates "y< 3x+ 8" from "y> 3x+ 8". The graph of "\(\displaystyle y\le 3x+ 8\)" is that line and the region below it. Mark that region by drawing, say, horizontal lines through it.
Similarly, if x= 0, y= -2(0)+3= 0+ 3= 3 and if x= 5, y= -2(5)+ 3= -10+ 3= -7 so (0, 3) and (5, -7) are points on the line y= -2x+ 3.
The line "y= -2x+ 3" separates "y< -2x+ 3" from "y> -2x+ 3". The graph or "\(\displaystyle y\ge -2x+ 3\)" is that line and the region above it. Mark that region by drawing, say, vertical lines through it.
The region in which both inequalities are true, the "solution to the system of inequalities" is the region that has both horizontal and vertical lines.