Question

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

Answer 1

Answer:

The solution will not change.

Step-by-step explanation:

Let y > 2x + p and y < 2x + p,

Where, p is any constant,

∵ If we subtract any number on both sides of an equality, the sign of inequality does not change,

i.e. y - p > 2x   and  y - p < 2x

$\implies \frac{y-p}{2} > x\text{ and }\frac{y-p}{2} < x$

$\implies x\in (-\infty, \frac{y-p}{2})\cap (\frac{y-p}{2}, \infty )-----(1)$

Similarly, If the inequality is,

$y < 2x + p\text{ and }y > 2x + p$

$\implies \frac{y-p}{2} < x\text{ and }\frac{y-p}{2} > x$

$\implies x\in (-\infty, \frac{y-p}{2})\cap (\frac{y-p}{2}, \infty )-----(2)$

From equation (1) and (2),

It is clear that, the solution will not change after reversing the sign of inequality.

Answer 2

Answer:

The System of inequality is ,

1. y > 2 x + p

2. y < 2 x + p

Suppose we assign some values to p and q and draw its graph

And, then the inequality sign on both inequalities is reversed

3. y < 2 x + p

4. y > 2 x + p

And , then draw it's graph

it has been found that, the solution set of both the inequality remains same.That is there is no point or set of points , which satisfy both the system of inequality.

The system has no solution.