Systems of Equations

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

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

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

• Parallel lines
• the same line 
• Intersecting lines

How many solutions?

• One Solution
• No solution
• Infinitely Many Solutions

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. 

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

• yes
• no

Solve the system of equations
y = 2x + 1
y = 4x - 1

• (1,3)
• (-1,-3)
• (-1,3)
• (3,1)

Solve the system of equations
y = 5x + 1
y = 3x + 13

• (6, 31)
• (31, 6)
• (4, 21)
• (2, 11)

Solve for x and y.
y = 2/3x - 2
y = -x + 3

• (0,3)
• (0,-3)
• (3,0)
• (-3,0)

Solve the system of equations.
y = 4x+1
3x + 2y = 13

• (1, 5)
• (5, 1)
• (0.25, 2)
• ∅

Solve for x and y using the substitution method.

5x + 3y = 7

y = 4

• (4,1)

• (4,-1)

• (1,4)

• (-1,4)