Elimination Method: Solving the System of Linear Equations 5x - 2y = 4 and 3x + y = 9
In this article, we will learn how to solve a system of linear equations using the elimination method. We will use the equations 5x - 2y = 4 and 3x + y = 9 as an example.
What is the Elimination Method?
The elimination method is a technique used to solve systems of linear equations by eliminating one variable at a time. This method involves adding or subtracting equations to eliminate one variable, and then solving for the other variable.
Solving the System of Equations
Let's start by writing the two equations:
Equation 1: 5x - 2y = 4 Equation 2: 3x + y = 9
Our goal is to eliminate one variable, say y, by making the coefficients of y in both equations equal but opposite in sign.
Step 1: Multiply both equations by necessary multiples
To make the coefficients of y equal but opposite in sign, we will multiply Equation 1 by 1 and Equation 2 by 2.
New Equation 1: 5x - 2y = 4 New Equation 2: 6x + 2y = 18
Step 2: Add both equations to eliminate y
Now we will add both equations to eliminate y.
5x - 2y = 4 6x + 2y = 18
11x = 22
Step 3: Solve for x
Now we have a simple equation in terms of x. Let's solve for x.
11x = 22 x = 22/11 x = 2
Step 4: Substitute x into one of the original equations to solve for y
Now that we have the value of x, we can substitute it into one of the original equations to solve for y. Let's use Equation 2.
3x + y = 9 3(2) + y = 9 6 + y = 9 y = 9 - 6 y = 3
Step 5: Write the solution
The solution to the system of equations is x = 2 and y = 3.
Therefore, the elimination method provides us with a simple and efficient way to solve systems of linear equations. By following these steps, we can solve for the variables x and y in the given equations.
