Learning Objectives:

__Math Tutoring on Solving Systems of Equations by Graphing__

**Two** **linear equations** that relate the **same two variables** are called a **system of equations.** A** **solution to a **system of linear equations **is an **ordered pair** that satisfies both equations. So for this system, a solution would be in the form of **(x, y),** where this ordered pair would satisfy both the first equation and the second equation. To solve a **system of linear equations by graphing**, we graph both linear equations on the same coordinate plane. There are three types of solutions to a **system of linear equations: **

**1)** We can have one **unique solution**, which means when we graph the two lines, the lines intersect at exactly one point. The solution would be the ordered pair of this point and because we have one solution, we say the system is **consistent **and** independent. **

**2)** We can also have **no solution** to our system. This occurs when the two lines are parallel and will never intersect. We can say the system is **inconsistent. **

**3)** We have **infinitely many solutions**. This occurs when both lines graph as the same line. So if we graph both lines, and they coincide and are on top of each other and we can say the system is **consistent **and **dependent.**

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**Hook Questions:**

*1. **When can we have a unique solution for a system of equations? *

*2. **What is meant by the statement there are infinitely many solutions for a system of equations.*

*3. **When will there be no solutions for a system of equations? *

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