 ## Substitution Method

In substitution method, one variable is expressed in therms of another variable from one equation and it is substituted to another equation. And it is solved to find the value of one variable. Then, it is  substituted to previous equation to find the value of another variable.

We use the following steps to solve the simultaneous linear equations by substitution method:

Steps:
i.         Convert any one variable of any one equation in the form of other variable.
ii.        Substitute value of one variable in another equation.
iii.       Simplify the equation, then we will get the value of one variable.
iv.       Substitute to calculate the value of the variable obtained in another equation and solve to get the value of another variable.

Things to remember:
-     Solve any one equation either for x or y.
-     Then, substitute the value of x or y in the next equation and solve it.

Workout Examples
Example 1: Solve: x = 3y and 4x + y = 26 by substitution method.
Solution: Here,
x = 3y ………… (i)
4x + y = 26 ………… (ii)

Substituting the value of x from equation (i) to equation (ii) we get,
4 × 3y + y = 26
or,     12y + y = 26
or,     13y = 26
or,     y = 26/13
or,     y = 2

Again, substituting the value of y = 2 in equation (i) we get,
x = 3 × 2
or,     x = 6

Hence, x = 6 and y = 2

Example 2: Solve: 2x + y = 180 and x + 2y = 240 by substitution method.
Solution: Here,
2x + y = 180 ………………… (i)
x + 2y = 240 ……………….. (ii)

From equation (i),
y  = 180 – 2x ………………. (iii)

Substituting the value of y from equation (iii) to equation (ii), we get,
x + 2 (180 – 2x) = 240
or,     x + 360 – 4x = 240
or,     – 3x = 240 – 360
or,     – 3x = – 120
or,     x = – 120 / –3
or,     x = 40

Again, substituting the value of x = 40 in equation (iii) we get
y = 180 – 2 × 40
= 180 – 80
= 100

Hence, x = 40 and y = 100

Example 3: Solve: 3x – 2y = 5 and 7x + 3y = 27 by substitution method.
Solution: Here,
3x – 2y = 5 ………… (i)
7x + 3y = 27 ………… (ii)

From equation (i)
3x = 5 + 2y

or,        35 +14y + 9y = 27 × 3
or,        23y = 81 – 35
or,        y = 46/23
or,        y = 2

Again, substituting the value of y = 2 in equation (iii) we get,
x = (5+2×2)/3
or,        x = 9/3
or,        x = 3

Hence, x = 3 and y = 2

You can comment your questions or problems regarding the solving of simultaneous linear equations by substitution method here.