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……………………….. (ii)

From eq. (i)

Substituting in eq.(ii)
By solving we get,
Substituting the value of y in eq.(i)

Then required fraction = =

Elimination Method:

Step 1- First multiply both the equations by some suitable non-zero constant to make
the coefficient s of any one variable 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 you get a true statement involving no variable, then the pair of equations has
infinitely many solutions.
(iii) If you get a false statement involving no variable, then the pair of equations has
no solution, i.e. it is inconsistent.

Step 3- Solve the equation in one variable so obtained to get its value.

Step 4 : Substitute the value of the variable obtained, in either of the original equation
to obtain the value of the other variable.

Example : Solve the following system of equations using the method of elimination

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