Number of solutions to a system

Presentation

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Mathematics

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8th Grade

•

Practice Problem

•

Medium

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CCSS

8.EE.C.8B, 8.EE.C.8A

Standards-aligned

Amanda Stefanik

Used 8+ times

FREE Resource

12 Slides • 14 Questions

Solving Systems of Equations by Graphing

Algebra 1

System of Equations: Types of Solutions

System of Equations

Two (or more) equations with the same variables
Example: y=2x+7 and y= -4x-2
Note that both equations have the same variables (x and y)

Multiple Choice

When you graph the exact same equation twice,

you will have no solution.

you will have one solution.

you will have infinite solutions.

you will have two solutions

Multiple Choice

How many solutions will this system have?

No solution

One Solution

two solutions

Infinitely Many Solutions

Multiple Choice

If a system of linear equations has one solution, what does this mean about the two lines?

Parallel lines

the same line

Intersecting lines

Multiple Choice

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

intersecting lines

parallel lines

skew lines

intersecting lines

Multiple Choice

How many solutions does this system have?

One

Two

No Solution

Infinitely Many Solutions

Multiple Choice

What is the number of solutions to the system of equations?

No Solution

Infinitely Many Solutions

One Solution

Two Solutions

Multiple Choice

How many solutions?

One Solution

No solution

Infinitely Many Solutions

Answering without doing (much) work

How can you tell how many solutions (0, 1, infinite) a system has without to much, if any, work? It is simple! Focus on the slopes

Same y+

Same slope=

parallel=

no solution

Same y+

Different slope=

intersecting=

one solution

Same everything=

same line=

infinite solutions

If they aren't

the same form-

get them the same

Multiple Choice

How many solutions does this system have?

y = x + 2

y = 3x - 2

One solution

No solution

Infinite solutions

Multiple Choice

How many solutions does this system have?

y = 2x + 4

y = x + 2

One solution

No solution

Infinite solutions

Multiple Choice

How many solutions does this system have?

y = 2x + 2

y = 2x - 1

One solution

No solution

Infinite solutions

Multiple Choice

How many solutions does this system have?

x - 2y = - 2

y = 1/2x + 1

One solution

No solution

Infinite solutions

Multiple Choice

How many solutions does this system have?

Infinite number of solutions

one solution

two solutions

no solution

Multiple Choice

How many solutions does this system have?

y=3x+2

y=2x+3

1 solution

No solutions

Infinite solutions

Multiple Choice

Is (20, -3) a solution to the system shown?

Yes

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

Solving Systems of Equations by Graphing

Algebra 1

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