- Graphical Method of Solving a System of Linear Equations
In this method there are three conditions
(1)Condition- `a_1/a_2` is not equal to `b_1/b_2`
Example- `2x+9y+12=0` and `6x+1y+8=0`
`2/6` is not equal to `9/1`
If we represent this equations on graph then the lines of this equation will intersect each other at some point.
In this condition we can conclude-
1) We get Intersecting line.
2) Such type of pair of linear eaquation with two variable where `a_1/a_2` is not equal to `b_1/b_2` have only one solution i.e unique solution.
3) This type of equations are called Consistent equations.
(2)Condition- `a_1/a_2`= `b_1/b_2`= `c_1/c_2`
Example- `2x+4y+8=0` and `6x+12y+24=0`
`2/6=1/3, 4/12=1/3, 8/24=1/3` i.e `1/3=1/3=1/3`
In the graphical representation of this equations the lines wil Coincide.
Thus the conclusion in this condition is-
1) We get conincent lines.
2) Such type of pair of linear eaquation with two variable where `a_1/a_2=b_1/b_2=c_1/c_2` have infinitely many soultions.
3) This equation is also called as Consisitent equations.
(3) Condition- `a_1/a_2= b_1/b_2` is not equal to `c_1/c_2`
Example- `2x+3y+4=0` and `4x+6y+7=0`
`2/4=1/2, 3/6=1/2, 4/7` i.e `1/2=1/2` is not equal to `4/7`
The graphical representation of these equations will result in parellel lines.
Here the conclusion is-
1) We will get Parellel.
2) Such type of pair of linear eaquation with two variable where `a_1/a_2= b_1/b_2` is not equal to `c_1/c_2` have no solution.
3) This type of Linear equations which dont give any solution are called as Inconsistent equations.
Shaalaa.com | Linear Equations 2 variables Part 2 Graphical
Draw the graphs representing the equations 4x + 3y = 24 and 3y=4x+24 on the same graph paper. Write the co-ordinates of the point of intersection of these lines and find the area of triangle formed by these lines and the X-axis.
Write the equation of X-axis. Hence, find the point of intersection of the graph of the equation x + y = 5 with the X-axis.
Draw the graph of x + y = 6 which intersects the X-axis and the Y-axis at A and B respectively. Find the length of seg AB. Also, find the area of Δ AOB where point O is the origin.
Complete the following table to draw the graph of 3x - y = 2