Question

Graph the solution of the following system of inequalities in the coordinate plane

Answer 1

The graph is attached here:

Explanation:

Answer 2

Given Inequalities are,

`y>(1)/(4)x+6`

`y>2x-1`

We need to graph the in equality.

First we find the point to draw the lines of the inequality.

By taking them equal we find point.

Consider,

`y=(1)/(4)x+6`

put, x = 0 ⇒ y = 6

put x = 4 ⇒ y = 1 + 6 = 7

So point to draw first line ( 0 , 6 ) and ( 4 , 7 )

Now Consider,

y = 2x - 1

put , x = 0 ⇒ y = -1

put , x = 4 ⇒ y = 8 - 1 = 7

So Points of the second line is ( 0 , -1 ) and ( 4 , 7 )

Since, the inequalities are strict then in graph lines drawn is dotted line as point on line does not includes in the inequality.

For Inequality put ( 0 , 0 )

`y>(1)/(4)x+6`

`0>6`

origin does not satisfy it. So, Region we shade is opposite to side in which origin belong.

`y>2x-1`

`0>-1`

origin does satisfy it. So, Region we shade is to side in which origin belong.

Therefore, The graph we get is attached.