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

Step-by-step 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

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1