Question

Which graph shows the solution to the system of linear inequalities below?

Answer 1

The correct graph is:

Graph B

Explanation:

First inequality is given by:

`y>(-1)/(3)x+1`

The inequality is a straight line that passes through (0,1) and (3,0) and also the line is dotted since the inequality is strict.

The shaded region is away from the origin since the inequality does not pass the zero point test.

Second inequality is given by:

`y>2x-1`

The graph of this inequality is a dotted line (since the inequality is strict) and passes through (0,-1) and (1/2,0) and the shaded region is towards the origin

( since the line passes the zero point test )

Graph B represents the system of inequality.

Answer 2

Option B

The solution in the attached figure

Explanation:

we have

Inequality A

`y > -(1)/(3)x+1`

we know that

The solution of the inequality A is the shaded area above the dashed line

The equation of the dashed line is
`y=-(1)/(3)x+1`

The slope of the dashed line is negative
`m=-(1)/(3)`

Inequality B

`y > 2x-1`

we know that

The solution of the inequality B is the shaded area above the dashed line

The equation of the dashed line is
`y=2x-1`

The slope of the dashed line is positive
`m=2`

therefore

The solution in the attached figure