Solving Systems of Linear Equations by Elimination Method: An Example
In this article, we will demonstrate how to solve a system of linear equations using the elimination method. The system of equations we will be working with is:
Equation 1: 3x - 5y - 4 = 0 Equation 2: 9x = 2y + 7
Step 1: Write the Equations
First, let's write the given equations:
3x - 5y - 4 = 0 ... (1) 9x = 2y + 7 ... (2)
Step 2: Convert Equation 2 to the Standard Form
We will convert Equation 2 to the standard form by subtracting 2y from both sides:
9x - 2y = 7 ... (2')
Step 3: Make the Coefficients of y's Opposite
To eliminate the y variable, we need to make the coefficients of y's opposite in both equations. We can do this by multiplying Equation 1 by 2 and Equation 2' by 5:
6x - 10y - 8 = 0 ... (1') 45x - 10y = 35 ... (2'')
Step 4: Add the Equations
Now, add Equation 1' and Equation 2'':
(6x - 10y - 8) + (45x - 10y = 35)
Combine like terms:
51x = 27
Step 5: Solve for x
Now, solve for x:
x = 27/51 x = 9/17
Step 6: Substitute x into One of the Original Equations
Substitute the value of x into one of the original equations to solve for y. We will use Equation 1:
3x - 5y - 4 = 0 3(9/17) - 5y - 4 = 0
Simplify and solve for y:
y = 11/17
Step 7: Write the Solution
Therefore, the solution to the system of linear equations is:
x = 9/17 y = 11/17
We have successfully solved the system of linear equations using the elimination method.
