Systems of Equations with special solutions

Systems of Equations

When 2 lines are drawn on the same graph, there are 3 possible outcomes.

• The lines intersect

• The lines are on top of each other

• The lines don't intersect

When we have two or more linear equations working together, we have a System of Equations.

• A solution to a system of equations is an ordered pair that makes both equations true.

• On a graph, this ordered pair is the point of intersection of the lines

Multiple Choice

In the situation in which Pele gets a head start, but Ronaldo catches up and passes, this is an example of a system of equations that has:

• One solution

• No solutions

• Infinite solutions

Multiple Choice

In the situation in which Pele and Ronaldo start in the same place and run the whole way together, this is an example of a system of equations that has:

• One solution

• No solutions

• Infinite solutions

Multiple Choice

In the situation in which Pele got a head start but he and Ronaldo were running at the same pace so Ronaldo never caught up, this is an example of a system that has:

• One solution

• No Solutions

• Infinite solutions

Multiple Choice

What is the solution to the system?

• (3,1)

• (1,3)

• (0,4)

• (-1,3)

Multiple Choice

Parallel Lines never intersect because...

• They have different slopes

• They have the same y-intercept

• They have the same slope

• They have different y-interceps

Multiple Choice

How many solutions does this system have?

• One solution

• No solutions

• Infinite solutiosn

Multiple Choice

How many solutions does this system have?

y=3x+2

y=2x+3

• 1 solution

• No solutions

• Infinite solutions

Multiple Choice

The ordered pair that makes BOTH equations true in the system is called the _____________________

• Graph

• System

• Solution

• Slope

Multiple Choice

Is (2,3) a solution for this system of equations?

y=3x

y=7x-8

• Yes

• No

• Sometimes

Multiple Choice

Is the ordered pair (-3, -7) a solution to the following system?

y = 4x + 5

y = x – 4

• Yes

• No

• All ordered pairs are solutions

• This system has NO Solutions

Multiple Choice

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

• Intersecting lines

• Parallel Lines

• 2 lines

• The same line

Multiple Choice

What is the solution to this system?

• (-1,1)

• (1,-1)

• (0,1)

• (1,0)

Multiple Choice

When you graph the exact same equation twice,

• You will have 1 solution

• You will have no solutions

• You will have infinite solutions

Poll

I understand that a system of linear equations can have one solution, infinitely many solutions, or no solutions.

• I got it!

• Kind of

• Not at all, I need to re-do this quizizz