In this post, we will explore the elimination method for solving systems of linear equations. This method involves adding, subtracting, or multiplying the equations to eliminate variables. Let's dive in with an example.

Example:

Consider the system of equations:

2x + 3y = 8
5x - 2y = 1

To eliminate the variable y, we can multiply the first equation by 2 and the second equation by 3. This way, the coefficients of y in both equations will be the same:

4x + 6y = 16
15x - 6y = 3

Now, we can add the two equations together to eliminate y:

4x + 15x = 16 + 3
19x = 19
x = 1

Plugging the value of x into one of the original equations, we can solve for y:

2(1) + 3y = 8
2 + 3y = 8
3y = 6
y = 2

Therefore, the solution to the system of equations is x = 1 and y = 2.

By using the elimination method, we can systematically solve systems of linear equations. This method is particularly useful when the coefficients of the variables can be easily made equal or differ by a multiple. Practice more examples to reinforce your understanding and gain confidence in solving systems of equations using elimination.

Remember, practice makes perfect!