Pair of Linear equations in Two Variables:
The chapter 'Pair of Linear Equation in Two variables' carrying the weightage of \(6\) marks in the board examination. It covers the concepts like Graphical method of soving pair of linear equations, Algebraic method of solving pair of linear equations - Substitution method, Elimination method.
Most possible variation of question types that we can expect in board exam as per previous year question paper are discussed below.
| Total Marks \(6\) |
||
| Variation \(1\) | Variation \(2\) | Variation \(3\) |
Total Marks \(=\) \(6\)
|
Total Marks \(=\) \(6\)
|
Total Marks \(=\) \(6\)
|
To prepare well for the board examination, it is necessary to understand the following concepts clearly.
- Zeroes of a polynomial - Finding zeroes, Finding quadratic polynomial using zeroes
- Relationship between zeroes and coefficients - Sum and product of zeroes, Verifying the relation
- Geometrical meaning of zeroes - Finding number of zeros
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 |