Question

How will the solution of the system y > 2x + Two-thirds and y < 2x + One-third change if the inequality sign on both inequalities is reversed to y < 2x + Two-thirds and
y > 2x + One-third?

Answer 1

Answer:

The shaded area would reverse on both inequalities.

The graphs do not overlap until the signs are reversed.

There are an infinite number of solutions in the system once the signs are reversed.

There are no solutions before they are reversed.

Step-by-step explanation:

Answer 2

Answer:

From not having solution the system changed to have solution

Step-by-step explanation:

step 1

we have

$y>2x+\frac{2}{3}$ ----> inequality A

$y$ ----> inequality B

Solve the system of inequalities by graph

using a graphing tool

The system has no solution , because the dashed lines are parallel lines

see the attached figure N 1

step 2

we have

$y$ ----> inequality A

$y>2x+\frac{1}{3}$ ----> inequality B

Solve the system of inequalities by graph

using a graphing tool

The solution is the shaded area between the two dashed lines

see the attached figure N 2

therefore

From not having solution the system changed to have solution