Solve the following inequalities graphically in two-dimensional plane: \[x-y\le 2\] - Noon Academy

Solve the following inequalities graphically in two-dimensional plane:

$x-y\le 2$

Class 11 | Exercise 6.2 | Linear Inequalities | Maths | NCERT

Solve the following inequalities graphically in two-dimensional plane:

$x-y\le 2$

Solution:

The given inequality is

$x-y\le 2$

Let us draw a solid line

$x-y=2$

in the graph (∵

$x-y=2$

is included in the given question)

Let us Consider

$x-y\le 2$

A point

$(0,0)$

is selected

⇒

$(0)-(0)\le 2$

⇒

$0\le 2$

(this is true)

Therefore, the solution region of

$x-y\le 2$

is above the line

$x-y=2$

. (That is origin is included in the region)

The graph is represented as:

i

More Material

Find the angle between each of the following pairs of lines:

Find the coordinates of the foot of the perpendicular drawn from the point (1, 2, 3) to the line

Show that the lines and do not intersect each other.

Find the vector equation of the line passing through the point with position vector and parallel to the vector Deduce the Cartesian equations of the line.

A line passes through the point (2, 1, -3) and is parallel to the vector Find the equations of the line in vector and Cartesian forms.

A line passes through the point (3, 4, 5) and is parallel to the vector Find the equations of the line in the vector as well as Cartesian forms.

Evaluate:

Evaluate:

Evaluate:

If $f(x) = |x| - 3,find\mathop {\lim }\limits_{x \to 3} f(x)$

Let $\begin{array}{l} f(x) = \left\{ \begin{array}{l} \frac{x}{{|x|}},x \ne 0\\ 0,x = 0 \end{array} \right.\\ \end{array}$ . Show that $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} f(x) \end{array}$ does not exist.

Let $\begin{array}{l} f(x) = \left\{ \begin{array}{l} \frac{|x-3|}{{(x-3)'}},x \ne 3\\ 0,x = 3 \end{array} \right.\\ \end{array}$ . Show that $\begin{array}{l} \mathop {\lim }\limits_{x \to 3} f(x) \end{array}$ does not exist.

← Previous Next →