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Elimination Calculator
To use the elimination calculator, enter the equations separated by semi-colon and hit the calculate button.
Elimination Calculator With Steps
Elimination calculator is used to find the unknown values of the system of linear equations with steps. This elimination method calculator takes the linear equations and gives the step-by-step solution in a couple of seconds.
What is the elimination method?
The elimination method is a method used to solve the system of linear equations. It is widely used to find the values of the unknown variables of linear equations. A single equation can be obtained by adding or subtracting equations in the elimination method.
In order to eliminate a variable, you add the equations when the signs of its coefficients are opposite, and subtract the equations when the signs of its coefficients are equal.
How to use the elimination method?
The elimination method calculator above can be used to apply the elimination method to the system of linear equations. If you want to learn how to apply the elimination method manually, follow the below example.
Example 1
Find the unknown values x & y by using the elimination method.
5x + 4y = 12
4x + 4y = 6
solution
Step 1: As the coefficients of y have the same values and same signs, so we'll subtract the given linear equations.
5x + 4y = 12
-(4x + 4y = 6)
x + 0 = 6
x = 6
Step 2: Now substitute the value of x in any given linear equation to get the result of y.
5x + 4y = 12
5(6) + 4y = 12
30 + 4y = 12
4y = 12 - 30
4y = -18
y = -18/4 = -9/2
y = -4.5
Example 2
Solve the system of linear equations by elimination method.
3x + 2y = 6
4x - 3y = 4
solution
Step 1: Multiply both linear equations with a suitable integer to make one variable the same.
Multiply "3x + 2y = 6" by 3
3(3x + 2y) = 3 * 6
9x + 6y = 18
Multiply "4x - 3y = 4" by 2
2(4x - 3y) = 2 * 4
8x - 6y = 8
Step 2: Now eliminate "y" by adding the linear equations.
9x + 6y = 18
8x - 6y = 8
17x + 0 = 26
x = 26/17
Step 2: Now put the value of "x = 26/17" to find the value of "y"
3x + 2y = 6
3(26/17) + 2y = 6
78/17 + 2y = 6
78/17 + 2y = 6
2y = 6 - 78/17
2y = (106 - 78)/17
2y = 24/17
y = 12/17
References
- What is the elimination method? Mathplanet. (n.d.).
- How to use the elimination method? (n.d.).