Solution of System of Linear Inequalities in 2 Variables Video Lecture | Mathematics (Maths) for JEE Main & Advanced

hi I'm George Woodbury from the college
of the Sequoias in Visalia California
and in this video I'll be talking about
linear inequalities in two variables and
how to graph them we begin by graphing
the line that's associated with the
inequality if the inequality involves
the symbol less than or equal to or
greater than or equal to we'll graph the
line using a solid line if the
inequality is a strict inequality
involving the symbols just less than or
greater than then the line is it going
to be graphed using a dashed line we'll
go ahead and select a test point that's
not on the line and we'll substitute the
coordinates for x and y in the original
inequality if the test point is a
solution will shade the half-plane that
contains the test point if it's not a
solution will shade the opposite side
let's take a look at a few examples
we're going to begin by graphing 2x
minus 3y is less than 6
notice the inequality symbol is less
than not equal to so we'll go ahead and
graph this using a dashed line this
equation would be in standard form so
it's going to be easier to graph using
the intercepts the x-intercept
substituting 0 for y 2x equals 6 or x
equals 3
if we substitute 0 for X we have
negative 3y equals 6 or y equals
negative 2 let's go ahead and take a
look at the graph and notice that the
origin 0 0 is not on the graph of this
line that's an ideal candidate for the
test point let's go ahead and see if 0 0
is a solution if it is we will shade the
top left portion of this graph if it's
not a solution we're going to go ahead
and shade the bottom right portion
substitute 0 for X and 0 for Y we end up
with the inequality 0 is less than 6
which is true that tells us to shade the
side of the line that contains the test
point 0 0 again our test point gave us a
true inequality we will shade the side
of the line that contains the test
if this inequality had been false we
would shade the other side let's try
another one first thing to notice here
is the equal sign under the greater then
that tells us to graph a solid line
second this is in slope-intercept form
we know the slope of this line is 1/8
and the y-intercept is at zero - that
would be the most efficient way to graph
this line taking a look at the graph
y-intercept of 0 2 up 1 8 to the right
draw the line that passes through them
again notice 0 0 the origin is not on
the line that's an ideal test point when
we substitute 0 for X and 0 for y we're
left with the inequality 0 is greater
than or equal to 2 which is false so
instead of shading the side that
contains the origin we're going to shade
the other side of this line right not
where the test point was but on the
other side of the line let's try one
more y is greater than 4x plus 20 this
line will be dashed no equal sign and
we'll graph the line using the slope
intercept form the y intercept is at 0
20 and the slope is 4 so starting at the
y intercept of 20 we move up for one to
the right notice that the vertical scale
here is in units of 4 and we draw the
dashed line that passes through them
again the origin is not on the line so
we'll use that for our test point when
we substitute in we are left with the
inequality 0 is greater than 20 which is
false that tells us to shade the other
side of the line here that's going to be
the top left if you have any questions
or comments on linear inequalities and
two variables go ahead and visit my
contact page at my website
George would very calm thanks for
watching