Question

Graph the solution to the following system of inequalities. y>1/4x+6, y>2x-1

Answer 1

The solution of the system of inequalities is the region above the right line y=(1/4)x+6 to the left of x=4; and above the right line y=2x-1 to the right of x=4

Explanation:

The inequality y>(1/4)x+6 is the area above the right line y=(1/4)x+6

For x=0→y=(1/4)(0)+6→y=0+6→y=6; Point=(x,y)→Point=(0,6)

For x=4→y=(1/4)(4)+6→y=1+6→y=7; Point=(x,y)→Point=(4,7)

The inequality y>2x-1 is the area above the right line y=2x-1

For x=0→y=2(0)-1→y=0-1→y=-1; Point=(x,y)→Point=(0,-1)

For x=4→y=2(4)-1→y=8-1→y=7; Point=(x,y)→Point=(4,7)

Graphing the right lines (see the attached file), we can see the solution of the system: The region above the right line y=(1/4)x+6 to the left of x=4; and above the right line y=2x-1 to the right of x=4