Systems of Equations

Steffen graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-3,-8)
• (-8,-3)
• (3,-8)
• (8,3)

Solve for x and y
2x − 3y = −1
 y = x − 1

• (-2,-3)
• (0,-1)
• (3,4)
• (4,3)

What is the solution to the system?

• (0, 3)
• (1, -1)
• (-3, 1)
• (1, 3)

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

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. 

How many solutions?

• One Solution
• No solution
• Infinitely Many Solutions

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

• (0,3)
• (0,-3)
• (3,0)
• (-3,0)

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

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

Solve the following system by setting the two equations equal to each other.  What is the solution?
HINT:  - 1/3x + 4 = 2/3x + 1 and then solve for x.  Once you find x go back and find y.

• Infinite number of solutions
• (3, 3)
• (3, -3)
• (-3, 3)

What is the solution to the system of equations? 
y = 3x - 8
y = 4 - x

• (3,1)
• (1,3)
• (-3,1)
• (3,-1)