Elimination Calculator

Elimination Calculator

The elimination calculator will solve two linear equations using the linear combination method. It gives the values of the variables present in both equations.

This elimination solver includes a math keyboard to enter arithmetic operations. Users can also see the whole method of the elimination process. 

What is the elimination method?

The elimination method is used to simplify two or more mathematical equations to calculate the value of the unknown variables. It has other names like addition or combination method as well

In this particular way of solving, two equations are written on top of each other and added. The equations are multiplied with such suitable numbers that one of the variable terms is cancelable.

After cancellation, the equation is added and solved to find the value of the remaining variable. The value of the known variable is then put in one of the equations to find the canceled variable’s value.

Solving equations by elimination

The manual process of applying the elimination method to the equations is

1. Arrange both equations and place them on each other such that the same variables are in a column. 
2. Add them after multiplying with such a number that makes the coefficients of one of the variables equal. 
3. Cancel the equal terms.
4. Solve to find the value of the remaining variable. 
5. Put the value of this variable in either equation 1 or 2.
6. Solve to find the other variable.    

Example:

Find the value of x and y in the following equations:

2x - 7y = 10

3y + 10x = 2

Solution:

Step 1:  Arrange the equations for addition. 

    2x - 7y = 10   … (1)

+  10x + 3y = 2 … (2)

Step 2: Multiply equation 1 by -5.

 -5(2x - 7y = 10) 

-10x + 35y = -50 

Step 3: Cancel the x variable as they are the same. 

-10x + 35y = -50 

 10x + 3y = 2

Step 4: Solve now.

35y = -50
3y = 2
______
38y = -48

y = -48/38

y = -24/19

Step 5: Put the value of y into equation (2).

10x + 3y = 2

10x + 3(-24/19) = 2

Solving fractions:

10x - 72/19 = 2 

10x = 72/19 x 2

Taking LCM.

10x = 110/19

x = 11/19

If you put these values of x and y in any of the two equations, the left-hand side and the right-hand side will be equal.