Slide 1 : MATHEMATICS
CLASS X
Slide 2 : PAIRS OF
LINEAR EQUATIONS
Slide 3 : General form a linear equation in two variables is of the form ax + by + c = 0
PAIRS OF LINES : PAIRS OF LINES Given a pair of lines in a plane,
a1x+b1y+c1=0 and a2x+b2y+c2=0
There are three situations.
The lines intersect at a single point.
The lines coincide or
The lines are parallel.
Solution : Solution The value of the variable which satisfies the given equation is called its solution.
For example, 2 is the solution of the equation 3x + 1 =7 as 3(2) + 1 = 7
Slide 6 : CONCLUSIONS
We can draw some conclusions
about the number of solutions
based on the number of points of
intersection of a pair of lines.
Slide 7 : 1) If a pair of lines intersect at a single
point then the system of equations has
a unique solution.
(solution will be the point of intersection)
Slide 8 : 2) If a pair of lines coincide then the
system of equations has infinite
number of solutions.
(every point on the line is a solution)
Slide 9 : 3) If the lines are parallel then the
system of equations has no solution.
(No common point as lines do not
intersect.)
Slide 10 : Given a pair of lines in a plane,
a1x+b1y+c1=0 and a2x+b2y+c2=0
If a1/a2 is not equal to
b1/b2 then the system has a unique solution.
Slide 11 : 2. If a1/a2 = b1/b2 = c1/c2
then the system has infinite solutions.
Slide 12 : 3. If a1/a2 = b1/b2 is not
equal to c1/c2 then the
system has no solution.