Number of solutions to a system

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

• No

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