Solving System of Equations by Graphing

4.1 Solving System of Equations by Graphing

​EQ: How do you use systems of equations and inequalities to model situations and solve problems?

When graphing, there are 3 types of solutions.

• One solution is where two lines intersect.

• Parallel lines have no solution.

• The same lines have infinite solutions.
  

One Solution

When two lines intersect at one point, this point is the solution to the system of equations.

Parallel Lines

• When two lines are parallel, they never intersect.

• Parallel lines have No Solution.
  

Infinitely Many Solutions

• When two lines are the same, they will have infinite 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

Multiple Choice

What is the solution?
(Hint:  Both lines are graphed over each other)

• One Solution
• No solution
• Infinitely Many Solutions

Multiple Choice

This system has _____ solutions

• no
• 1
• 2
• Infinitely many

Multiple Choice

What is the solution to this system of equations?

• (4, -1)
• (-1, 4)
• (-4, 1)
• (-4, -1)

Multiple Choice

What is the solution to the system?

• (0, 3)
• (1, -1)
• (-3, 1)
• (1, 3)

Multiple Choice

The solution to this system of equations is:

• (4, 3)
• (3, 4)
• (-4, 3)
• No solution

Poll

How do we feel about the topic of Solving Systems of Equations by Graphing?

• Great! I get it! :)

• Eh, I think I get it. Need practice.

• I'm not sure I understand :/

• HELP!!!!