Question

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

Answer 1

Answer:

The graph is attached here:

Step-by-step explanation:

Answer 2

Answer:

Given Inequalities are,

$y>\frac{1}{4}x+6$

$y>2x-1$

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,

$y=\frac{1}{4}x+6$

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 )

$y>\frac{1}{4}x+6$

$0>6$

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.