Explain the elimination method of linear equation in 2 variables with an example.
The linear equations in two variables are of the highest exponent order of 1 and have one, none, or infinitely many solutions. The standard form of linear equation is ax + by + c = 0, where x and y are the two variables.
Answer: The elimination method is one of the most widely used methods to solve a system of linear equations, where we eliminate any one of the variables and then find the value of the other variable.
Let's look into the stepwise solution.
The elimination method is one of the most widely used methods to solve a system of linear equations. The elimination method is widely used because in this method we eliminate one of the variables and do our calculations with only one variable quickly.
Let's take an example to understand this. We will find the value of x and y from the set of linear equations given below:
x+y=9 __ (1)
x-y=5 __ (2)
Step 1: Select a variable which you want to eliminate from the equations.
Let us select y.
Step 2: Take suitable constants and multiply them with the given equations so as to make the coefficients of the variable (which we want to eliminate) equal.
Here, the coefficients of variable y in both the equations are equal, so we can skip this step.
Step 3: Add or subtract the two equations obtained and eliminate one variable.
Here, on adding the equations (1), and (2), we get,
Step 4: Solve the equation to find the value of the remaining variable.
On solving 2x=14, we get,
x = 7 (as you can see in the figure above)
Step 5: Substitute the value of the variable to find the value of the other variable.
On substituting the value of x in equation (1), we get,
7 + y = 9
⇒ y = 9 - 7
⇒ y = 2
Therefore the value of x = 7 and y = 2.