
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.
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