Lecture 7.1 - Solve Systems by Graphing

​7.1 - Graphing Systems of Equations

Two linear equations... on the same graph? Slay, Mr. G. Slay.​

​System of Equations

→​ representation of two or more equations

Don't worry, you won't have 3 or more until Algebra 2​

​Solution to a System of Equations

→​ the point(s) at which a system of equations intersect

A point that works for two equations?!

​Consistent

→​ a system has at least one solution (intersection)

"Consintersection"? "Consistersection"?

​Independent

→​ a system has exactly one solution (intersection)

→​ they are 2 distinct lines
→ different slope

This will be the most common for us to solve​

​Dependent

​→ a system has infinite solutions (intersections)

​→ they're the same line
→ same slope, same y-intercept

Twinnin'

​Inconsistent

​→ a system has no solution (intersection)

​→ they're parallel lines
→ same slope, different y-intercept

They'll never meet :(

Flow charts 😍​

Multiple Choice

The following system will have how many solutions?

$$y=2x+1$$  

$$y=4x+1$$  

• One Solution

• No Solution

• Infinitely Many Solutions

• Cannot tell without graphing

Multiple Choice

Classify the system:

y = -³/₄x + 8

y = ¹³/₄x - 8

• Consistent Independent

• Consistent Dependent

• Inconsistent

Multiple Choice

Classify the system:

y = -x - 7

y = -x + 2

• Consistent Independent

• Consistent Dependent

• Inconsistent

Multiple Choice

Classify the system:

y = ²/₃x + 6

y = ²/₃x + 6

• Consistent Independent

• Consistent Dependent

• Inconsistent

Multiple Choice

Consistent or Inconsistent?

• Consistent
• Inconsistent

Multiple Choice

Consistent or Inconsistent?

• Consistent
• Inconsistent

Multiple Choice

Consistent or Inconsistent?

• Consistent
• Inconsistent

Multiple Choice

Consistent or Inconsistent?

• Consistent
• Inconsistent

Multiple Choice

Dependent or Independent?

• Dependent

• Independent

• Neither

Multiple Choice

Dependent or Independent?

• Dependent
• Independent
• Neither

Multiple Choice

Dependent or Independent?

• Dependent
• Independent
• Neither

Multiple Choice

Which system of linear equations has no solution?

Multiple Choice

Which system of equations has one solution?

Multiple Choice

A system of equations with infinitely many solutions will have lines that...

• are the same

• are parallel and never touch

• cross in one place

​Solve Systems by Graphing

​→ we can solve a system by locating the point of intersection given a graph or graph equations ourselves to find out where they intersect

GRAPH PARTY

Multiple Choice

What is the solution to the following system of equations?

• (0,3)

• (-3, 1)

• (1, 3)

• Infinitely Many Solutions

• No Solution

Multiple Choice

What is the solutions to the following system of equations?

• (5,2)

• (2, 5)

• (0,3)

• Infinity Many Solutions

• No Solutions

Multiple Choice

What is the solutions to the following system of equations?

• (0,3)

• (0,0)

• (-3,0)

• Infinity Many Solutions

• No Solution

Multiple Choice

How many solutions will this system have? 

• No solution
• One Solution
• (0,1)

• (-2,0)

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

Parallel Lines never intersect because...

• they have the same slopes. 
• they have the same y-intercept.
• they have different slopes.
• they have different y-intercepts. 

Draw

Solve the system of equations by graphing

y = 4x+3

y = -x-2

Draw

Solve the system of equations by graphing

$$y=-1$$  

$$\frac{5}{2}x+y=4$$  

Draw

Solve the system of equations by graphing

$$y=-x+4$$  

$$x+y=1$$