Systems of equations by elimination is a method used in algebra to solve a system of two or more equations. This method involves adding or subtracting the equations in order to eliminate one variable, which allows for the solution of the system. It is a powerful tool that can be used to find the intersection point of two lines or the solution to a system of linear equations.
When working with systems of equations by elimination, it is important to carefully manipulate the equations to ensure that one variable is eliminated. This can be done by multiplying one or both equations by a factor that will result in the coefficients of one variable being equal and opposite in sign. By adding or subtracting the equations, the variable will cancel out, leaving a new equation with only one variable.
For example, consider the system of equations:
2x + 3y = 7
4x – 2y = 2
To solve this system using elimination, we can multiply the first equation by 2 and the second equation by 3:
4x + 6y = 14
12x – 6y = 6
By adding these equations together, we eliminate the y variable:
16x = 20
x = 1.25
Substitute this value back into one of the original equations to solve for y:
2(1.25) + 3y = 7
2.5 + 3y = 7
3y = 4.5
y = 1.5
Therefore, the solution to the system of equations is x = 1.25 and y = 1.5. Systems of equations by elimination worksheets are a great way to practice this method and improve your algebra skills. They typically consist of a series of equations for students to solve using the elimination method, with varying levels of difficulty to challenge learners of all abilities.
Overall, systems of equations by elimination is a valuable tool in algebra that allows for the solution of systems of linear equations. By carefully manipulating the equations and eliminating one variable, the solution can be found. Practice with worksheets can help reinforce this method and improve problem-solving skills in algebra.