Systems of Linear Equations

Systems of Linear Equations

We will be able to identify and find a solution to a system of equations.

I will be able to take notes and participate in the Quizizz lesson.

WARM-UP

Answer the question on the next slide.

Multiple Choice

What kind of lines are these?

• Parallel lines

• Line segments

• Perpendicular Lines

• Intersecting lines

What is a system of Linear Equations?

A system of linear equations is 2 or more linear equations with the same variables.

Examples of Linear Equations

- 2 lines and the point where the 2 lines intersect is the solution. (2, 3)

Examples of Linear Equations

- 2 equations with the same variables

Solutions to Linear Equations:

• To find a solution to a system find the point where the 2 lines intersect.

• Also you can plug in the point (x,y) and if it makes both equations true then it is a solution.

• A system of linear equations has three types of solutions.

Multiple Choice

How many solutions will this system have? 

• No solution
• One Solution
• I Don't Know
• Infinitely Many Solutions

Multiple Choice

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

Multiple Choice

How many solutions does this system of equations have?

• One Solution
• No solution
• Infinitely Many Solutions
• Two Solutions

Multiple Choice

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

1.) Make sure the equations are in slope intercept form.(y=mx+b)

2.) Add a Graph on your calculator.

3.) Type the equations in the calculator. Press Tab to get the 2nd equation.

4.) Press Menu, 6:Analyze Graph, 4:Intersection

5.) Drag dotted line to shade in the point of intersection.

​Steps:

​Ex. 1:

Solving Systems of Equations by Graphing with Calculator

1.) Make sure the equations are in slope intercept form.(y=mx+b)

2.) Add a Graph on your calculator.

3.) Type the equations in the calculator. Press Tab to get the 2nd equation.

4.) Press Menu, 6:Analyze Graph, 4:Intersection

5.) Drag dotted line to shade in the point of intersection.

​Steps:

​Ex. 2:

Solving Systems of Equations by Graphing with Calculator

Multiple Choice

Solve the system of equations by graphing.

• (4, 7)

• (3, 5)

• (6, 7)

• (5, 3)