Category : 9th Class
LINEAR EQUATION IN TWO VARIABLES
FUNDAMENTALS
Example:- \[(i)\,\,3x+4y-2=0\]
\[\left( ii \right)\,\,4x+7y=3\]
Are the linear equations in x and y?
Solution:- Any point of values of x and y which satisfies the equation ax \[4x+by+=0\] is called a solution of it.
Example:- \[x=3,y=2\] is a solution of \[3x+2y=13\] because, when \[x=3\] and \[y=2,\] we have\[L.H.S=3\times 3+2\times 2=13=R.H.S\]
Example:- \[x+2y=7\]
X |
1 |
3 |
-1 |
-3 |
Y |
3 |
2 |
4 |
5 |
The graph of equation parallel to y-axis The graph of equation parallel to x-axis
\[x=2\] \[y=2\]
Then, we have the following situations.
Number of solution |
Condition |
Nature of graph lines |
(i) No solution |
\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] |
Parallel |
(ii) Unique solution |
\[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\] |
Intersect at a point |
(iii) Infinitely many solution |
\[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}}\] |
Coincident |
You need to login to perform this action.
You will be redirected in
3 sec