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Substitution Calculator
To use the substitution calculator, enter the linear equation separated by ";" and press calculate button
Substitution Method Calculator
Substitution method calculator is an online tool that is used to solve the system of linear equations. The substitution calculator will give a step-by-step solution.
What is the Substitution Method?
The substitution method is a mathematical technique that is used to solve a system of equations. In this method, isolate one variable from one equation (say “x”) and its value is substituted into the other equation of the same system.
Then evaluate the value of the other variable (say “y”) by substituting the equation using algebraic operation and this value is put into the first equation to evaluate the value of the first variable.
How to use the substitution method to solve linear equations?
Here is an example of solving a system of equations to explain the working of the substitution method.
Example:
Solve the given system of equations using the Substitution method.
x + 2y = -3
x - 3y = 2
Solution:
Step 1: write the above equation and give the name eq (i) & eq (ii).
x + 2y = -3------> (i)
x - 3y = 2--------> (ii)
Step 2: Solve the eq (i) for “x”.
x + 2y = -3
x = -3 - 2y
Step 3: Substitute the above value in eq (ii) and Simplify for “y”.
(-3 - 2y) –3 y = 2
-3 - 2y – 3y = 2
- 3– 5y = 2
– 5y = 2 + 3
– 5y = 5
y = 5/(-5)
y = - 1
Step 4: Put the above value of “y” in step 2 and simplify.
Put y = - 1
x = -3 - 2y
x = -3 – 2(-1)
x = -3 + 2
x = - 1
Hence,
x = -1, y = - 1 is the solution of the given system of linear equations.
Some other examples
Sytem of linear equations | Results |
x+y=5 ; x+2y=7 | x=3, y =2 |
-x-7y=-1 ; x-2y=-8 | x=−6, y=1 |
2x + y = 7 ;3x - 4y = 1 | x=38/11, y=1/11 |
2x – y = 3 ; x + 2y = 2 | x=8/5, y=1/5 |
x-3y = -43 ; 2x+2y=-41 | x=-209/8, y=45/8 |