# Substitution Method

**Elimination by Substitution**

In this method we first find the value of one variable (y), say in terms of x from the first equation and put this value of y in the second equation. Thus we get an equation in terms of x, which can easily be solved. The value of x is then put in the expression for y.Â Â Â Â Â

Â

Solve

Â Â (i) 2x - 3y = 5Â Â Â Â Â Â Â Â Â Â Â Â Â (ii) x + 2y = 5

Â Â Â Â Â Â 3x + 2y = 1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2x - yÂ = 5

(i) 2x - 3y = 5

Â Â Â Â Â â‡’Â Â y =

We substitute the value of y in

Â 3x + 2y = 1

â‡’Â Â 3x + 2() = 1

â‡’Â Â 9x + 2(2x-5) = 3

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â â‡’Â Â 13x = 13Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â â‡’Â Â Â Â x = 1

Putting this value of x in (ii) we get,

Â â‡’Â Â y =

Therefore, the solution is x = 1,y = -1

(ii)Â Â x + 2y = 5

Â Â Â Â Â Â Â Â Â Â Â Â Â Â x = 5 - 2y

We put this value of x in

Â Â Â Â Â Â Â Â Â Â Â 2x - y = 5

Â â‡’Â 2(5-2y) - y = 5

Â Â â‡’ 10 - 4y - y = 5

Â Â Â â‡’Â 10 - 5y = 5Â Â Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â y = 1

Putting this value of y in (ii), we get

Â x = 5 - 2(1) = 3

Therefore, the solution isÂ Â Â Â Â Â Â Â Â Â

x = 3, y = 1.