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:

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

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

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

Answer 2

Answer:

On changing inequalities one can have a particular region where the solution of equation lies hence, the inequalities converted from no solution to having a solution.

Step-by-step explanation:

Given information:

Two inequalities

$y>2x+\frac{2}{3} \\\\y<2x+\frac{1}{3}$

Now, On solving the above inequalities one can see that there is two parallel lines as solution.

Hence there is no solution for the inequalities because we are not getting any particular region in which our solution lies.

Now in the second case:

The inequalities changes to:

$y<2x+\frac{2}{3}\\\\y>2x+\frac{1}{3}$

On solving above inequalities we are having a particular region where the solution of equation lies.

Hence the inequalities converted from no solution to having a solution.

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