Solving Systems of Linear Equations by Graphing

02/27/18

Warm-Up Graph the following equation.

2𝑦 + 8𝑥 = 16

1.

2.

3.

Need an ID or Ruler for Todays Lesson

https://www.youtube.com/watch?v=1qHTmxlaZWQ

Objective

Students will be able to find the solution of a system of linear equations by graphing.

Vocabulary

System of linear equations also called a linear system, consists of two

or more linear equations that have the same variables.

Solution to an equation is any ordered pair that makes the equation true.

Solution of a system of linear equations with two variables is any ordered pair

that satisfies all of the equations in the system.

Example 1) Solve this system of equations by graphing.

𝑦 = 2𝑥 − 2

3𝑦 + 6𝑥 = 18

1.Graph both lines. 2. Find the point where both lines intersect.

Pair Share 1.Summarize in your own words how you solve by graphing.

2. How do you know which point is your solution?

Example 2) Solve this system of equations by graphing.

𝑦 = 2𝑥 − 2

−4𝑥 + 2𝑦 = 8

1.Graph both lines. 2. Find the point where both lines intersect. Pair Share: Discuss with your partner what your solution would be.

Example 3) Solve this system of equations by graphing.

𝑦 = 3𝑥 − 3

−6𝑥 + 2𝑦 = −6

1.Graph both lines. 2. Find the point where both lines intersect. Pair Share: Discuss with your partner what your solution would be.

Vocabulary

A inconsistent system: A system that has

no solution.

A consistent system: A system that has

at least one solution.

An independent system has exactly one solution.

A dependent system has infinitely many solutions.

Lines________________

Lines_________________ Lines__________________

Whiteboards Determine weather the following systems of linear equations have one solution, no solution or infinitely many solutions.

A one solution B no solution C infinitely many solutions.

A one solution B no solution C infinitely many solutions.

A one solution B no solution C infinitely many solutions

Exit Ticket 1. Solve this system of equations by graphing.

−𝑥 + 𝑦 = 32𝑥 + 𝑦 = 6