Systems of Linear Equations.

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 graph a giraffe. 

What are the three methods we have learned to solve Systems of Equations?

• Graphing, Substitution, and Elimination
• Drawing, Consolidation, and Emancipation
• Reading, Revocation, and Fluctuation
• Radicalizing, Reformation, and Graduation

How many solutions will this system have?

• One
• Two
• No Solution
• Infinitely Many Solutions

Find the solution:
2x-5y=15
3x+y=31

• (10,1)
• (13, -8)
• (-10,-7)
• No Solution

2x + y = 10
y = -2x + 13

• (-2, 17)
• (2, 6)
• no solution
• all solutions

This system has _____ solutions

• 0
• 1
• 2
• Infinitely many

x + y = -3
y = x - 5

• (1, -4)
• (-1, 4)
• all solutions
• no solution

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

• intersecting lines
• parallel lines
• perpendicular lines
• coinciding lines

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

• Parallel lines
• coinciding lines 
• Intersecting lines

Determine if (4, 1) is a solution for the system of equations.
y = -x + 5
y = 2x - 7

• yes
• no