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Linear Combination Calculator

# Linear Combination Calculator

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Linear combination is one of the methods to solve for the unknown variables in the given equations. In this

method one unknown variable is eliminated and the value of the remaining variable is calculated. The online

tool used to find the solution of two given equations using linear combination method is called the Linear

combination calculator.

Example 1: Find the solution of the two linear equations x + y = 10; x - y = 4.

Given are the equations with two unknown variables x, y.

Linear combination method can be used to solve for the two variables.

The co-efficient or ‘y’ in both the equations is 1, so subtract both the equation.

(x + y = 10) -  (x - y = 4) -> 2y = 6 -> y = 3.

Substitute y = 3 -> x + 3 = 10 -> x = 7.

Hence x = 7 and y = 3.

Example 2: Find the solution of the two linear equations 2x + y = 6; x - y = 6

Given are the equations with two unknown variables x, y.

Linear combination method can be used to solve for the two variables.

The co-efficient or ‘y’ in both the equations are 1 and -1, so add both the equation.

(2x + y = 6) + (x - y = 6) -> 3x = 12 -> x = 4.

Substitute x = 4 -> 4 - y = 6 -> y = -2.

Hence x = 4 and y = -2.