PAIR OF LINEAR EQUATIONS IN TWO VARIABLES : PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
Graphical Solution : Graphical Solution Every linear equation is one dimensional in nature.
Every linear equation represents a straight line.
To plot the Graph always take three points for reference. Two points to draw the straight line and third point to verify the plotting of straight line. Preferably, first two points to be taken as x = 0 & corresponding value of y and y = 0 & corresponding value for x.
As shown in the example. : As shown in the example. Example:
3x + 2y = 9
or, 2y = 9 – 3x
or, y = 9 – 3x
2
Slide4 : Plot the X & Y axes in the graph sheet.
Define and relate the small units of the graph and number taken
Draw the line with two of the points if third point lie on the straight line drawn then your plotting and calculation are correct.
Last but not at all the least, do remember to write the solution after lines are plotted in the graph.
Arithmetically solving the Equation:- : Arithmetically solving the Equation:- Elimination or Substitution Method
Equating the co-efficient
Cross Multiplication method
Elimination or Substitution Method : Elimination or Substitution Method In this method, we eliminate or substitute one of the variables; the same method we applied in graphical method. Then the value of y (or x) in terms of x ( or y) obtained from the 1st equation is put in the 2nd equation and subsequently solve it.
Equating the co-efficient : Equating the co-efficient In this method, we equate either of the co-efficient of two variables and by the subtraction of two equations we cancel the equated variable. Then we get the solution of the other variable and thereafter using the obtained solution we achieve the other variable also.
Cross Multiplication method : Cross Multiplication method In this method we can very easily and directly get the solution.
- Most important part of this method is choosing the format of the equation.
i.e.
Either, ax + by + c=0-------------(1)
or, ax + by = (-c) or c’-------(2)
We prefer to take the format (1) : We prefer to take the format (1)
Slide10 : Remember,
a, b, c are general co-efficient in the formula. These can be (+) ve or (-) ve any constant according to the question.
For practical problems in this chapter,
Read and understand the problem very clearly.
Detect the unknown identities and name them x, y etc
Identify the variables required to be solve.
Construct the equations according to the question.
Solve the equations in any of the comfortable method or as stated in the question.
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