(b) Elimination method: Following are the steps to solve the pair of linear equations by elimination method:
Step 1:First multiply both the equations by some suitable non-zero constants to make the coefficients of one variable (either x or y) numerically equal.
Step 2:Then add or subtract one equation from the other so that one variable gets eliminated.
(i) If you get an equation in one variable, go to Step 3.
(ii) If in Step 2, we obtain a true statement involving no variable, then the original pair of equations has infinitely many solutions.
(iii) If in Step 2, we obtain a false statement involving no variable, then the original pair of equations has no solution, i.e., it is inconsistent.
Step 3:Solve the equation in one variable (x or y) so obtained to get its value.
Step 4:Substitute this value of x (or y) in either of the original equations to get the value of the other variable.
(c) Cross multiplication method:By cross multiplication method, the value of x and y is as follows:
when a1b2 – a2b1 ≠ 0
Algebraic Methods of Solving a Pair of Linear Equations
Equations Reducible to a Pair of Linear Equations in Two Variables:
We have several situations which can be mathematically represented by two equations that are not linear, but we change them so that they are reduced to a pair of linear equations.
