Now, if we try to subtract equation 4 from equation 3, we get, 0=1 as both the variables are getting eliminated. In order to make the x coefficients equal in both the equations, we multiply equation (1) by 2 and equation (2) by 1. For example, let us solve two equations 2x - y = 4 → (1) and 4x - 2y = 7 → (2) by the elimination method. In such cases, we cannot eliminate only one variable. So, if we solve any such equations using the elimination method we get the answer as two unequal numbers on both sides of the unequal sign.

Elimination Method: No SolutionsĪs we know that equations of two parallel lines have no solutions. Let us discuss each of these two cases in detail. And the equations of coincident lines have infinitely many solutions as they lie on each other so every point is the intersection or the common point of those lines. Equations of two intersecting lines will have only two solutions that are consistent, but the equations of two parallel lines have no solutions as these lines never intersect each other. Step 3: Substitute the value of y in equation 1, we get, x + 12/5 = 8īut what if while multiplying a non-zero constant, we get the coefficients of both the variables equal? What if both the terms got eliminated while adding or subtracting? We get such cases while solving equations of parallel and coincident lines. Step 2: Subtract equation 2 from 1, we get, y=12/5. So, the two equations we have now are 2x + 2y = 16 → (1) and 2x - 3y = 4 → (2). Step 1: To make the coefficients of x equal, multiply equation (1) by 2 and equation (2) by 1. Let us take an example of two linear equations x+y=8 and 2x-3y=4 to understand it better. These are the elimination method steps to solve simultaneous linear equations. Step-4: At last, substitute this value in any of the given equations to find the value of the other given variable.

Step-3: Simplify the result to get a final answer of the left out variable (let's say, y) such that we will only get an answer in the form of y=c, where c is any constant.Step-2: Add or subtract both the equations such that the same terms will get eliminated.Step-1: The first step is to multiply or divide both the linear equations with a non-zero number to get a common coefficient of any one of the variables in both equations.Let us look at the steps to solve a system of equations using the elimination method. But it can only be applied to two equations at a time. We can solve three equations as well using this method. The elimination method is useful to solve linear equations containing two or three variables.

Elimination method system of equations