Systems of linear equations

Systems of EquationsA system is a pair or a group of equations.


Example of a system: 2x – y = 6

x – 5y = 3


Example of a system: 2x – y = 6

x – 5y = 3

Take note of the left brace.

This means that both equations are part of a system.

Systems of EquationsAn ordered pair is a solution to the system if it

satisfies all the equations.

Systems of EquationsAn ordered pair is a solution to the system if it

satisfies all the equations.

The solution set of a system is the set of all ordered pairs that satisfy the equations, or the set of all solutions.

Systems of Equations What is the solution to the system?


Can you think of an ordered pair that satisfies both equations?


The ordered pair (3, 0) is a solution.


The ordered pair (3, 0) is a solution.

Try to plug in (3, 0) in each equation.

Systems of EquationsThe solution to the system

is the ordered pair (3, 0).

SS: { }



SS: { (3, 0) }



But how do we get (3, 0)?



But how do we get (3, 0)? Recall: Activity in the Math Lab



But how do we get (3, 0)? Hmmm……

Systems of EquationsFind the solution to the system:

x + y + 4 = 0

x + 2y + 4 = 0

Systems of EquationsFind the solution to the system:

x + y + 4 = 0

x + 2y + 4 = 0

(Hint: Use Geogebra.)

Systems of linear equations

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