Let us recall the concepts in Pair of Linear Equation in Two Variables:
1. A pair of linear equations in two variables' can be represented, and solved, by the:
(i) graphical method
(ii) algebraic method
(i) graphical method
(ii) algebraic method
2. Graphical Method : The graph of a pair of linear equations in two variables is represented by two lines.
- When two lines in a graph intersect at only one point, then the graph is a consistent system and has one solution.
- When two lines in a graph do not intersect at any point, then the graph is an inconsistent system and has no solution.
- When two lines in a graph are identical at all points, the graph is a consistent system and has infinitely many points.
3. Algebraic Methods : We have discussed the following methods for finding the solution(s)
of a pair of linear equations :
(i) Substitution Method
(ii) Elimination Method
of a pair of linear equations :
(i) Substitution Method
(ii) Elimination Method
4. General form of the pair of linear equations in two variables:
\(a_{1}x+b_{1}y+c_{1}=0\)
\(a_{2}x+b_{2}y+c_{2}=0\)
| CONDITION | CONSISTENT OR INCOSISTENT | TYPE OF SOLUTION | GRAPHICAL REPRESENTATION |
| \(\frac{a_{1}}{a_{2}}\neq \frac{b_{1}}{b_{2}}\) | CONSISTENT | UNIQUE SOLUTION | INTERSECTING LINE |
| \(\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}= \frac{c_{1}}{c_{2}}\) | CONSISTENT | INFINITELY MANY SOLUTIONS | COINCIDE LINE |
| \(\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\) | INCONSISTENT | NO SOLUTION | PARALLEL LINE |