A system of linear equations comprises two or more linear equations with a common set of variables, where the goal is to find the point where the lines intersect. There are three possible outcomes when graphing two linear equations: 1) the lines intersect at a single point, indicating one solution; 2) the lines are parallel and do not intersect, indicating no solution; or 3) the lines coincide, indicating infinitely many solutions. Solving systems of linear equations algebraically or graphically allows determining the number and type of solutions.

2. A equation between two
variable that give a straight
line when plotted on a graph

4. Solving systems of equations in two
variables. A system of a linear
equation comprises two or
more equations and one seeks a
common solution to the equations. In
a system of linear equations,
each equation corresponds with a
straight line corresponds and one
seeks out the point where
the two lines intersect .

5. •One solution – The line cross at the one point.
•No solution – the line does not cross and it is parrell
•Many solution – The line concide each other

6. Sr.
No
Pair of eq. a1/a2 b1/b2 c1/c2 Compar
e the
ratio
Graphical
represent
ation
Algebraic
interpret
ation
1 x-2y=0
3x+4y-20=0
1/3 -2/4 0/-20 a1/a2#b1
/b2
Intersecting
lines
Exactly one
solution
(unique)
2 2x+3y-9=0
4x+6y-18=0
2/4 3/6 -9/-18 a1/a2=b1
/b2=c1/c
2
Coincident
lines
Infinitely
many
solution
3 X+2y-4=0
2x+4y-12=0
½ 2/4 -4/-12 a1/a2=b1
/b2#c1/c
2
Parallel lines No solution

7. Ex.1 :- Make a crossing graph on equation:-
x+3y=6
2x-3y=12
Solution:-
Firstly we have to find the solution of the equation and the
solution are :-
X+3y=6
X 0 6
Y=6-x
3
2 0

8. 2x-3y=12
X 0 3
Y=2x-12
3
-4 -2

9. Solve the equation and draw a graph
2x+3y=9
4x+6y=18
Solution:-
2x+3y=9
X 0 4.5
y=9-2x
3
3 0
X 0 3
Y=18-4x
6
3 1