Systems of Equations

Systems of Equations

By Mrs. Dockemeyer

Let's Review.....

When 2 lines are drawn on the same graph, there are 3 possible outcomes.

• The lines intersect

• The lines don't intersect

• The lines are on top of each other

For lines to intersect once...

• The place where the line intersects is at an ordered pair

• Write the orderd pair in the form of (x,y).

• The slopes of the two lines must be different.

For lines not to intersect at all...

• The lines must be parallel

• If the lines are parallel, we can write 'NO SOLUTION'

• Parallel lines have the SAME SLOPE but DIFFERENT y-intercepts

For lines to be right on top of one another...

• You should only see one line even though there are 2 equations.

• When this situation occurs, you can write "INFINITE SOLUTIONS"

• The 2 equations have to be mathematically the equal to one another for the lines to be on top of one another.

Multiple Choice

What is the point of intersection for the problem at the left, if any?

• (-3,0)

• (0,3)

• (3,0)

• (0,-3)

Multiple Choice

What is the point of intersection for the problem at the left, if any?

• (1,-1)

• (-1,-1)

• (1,1)

• (-1,1)

Multiple Choice

What is the point of intersection for the problem at the left, if any?

• (1,-4)

• (-1,-4)

• (-4,1)

• (-4,-1)

Multiple Choice

What is the point of intersection for the problem at the left, if any?

• (4,2)

• (-2,1)

• No Solution

• Infinite Solutions

Multiple Choice

Solve the system by graphing:
y = 6x - 4
y = -x + 3

• (1, 2)
• (2, 1)
• (4, 5)
• (2, 4)

Multiple Choice

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

• Parallel lines
• the same line 
• Intersecting lines

Multiple Choice

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

• Intersecting lines
• Same line
• Parallel lines

Multiple Choice

Solve this system of equations by graphing.

y = 1/2x + 2

y = -3x + 9

• (2, 3)

• (-2, -3)

• (3, 2)

• (-3, 2)

Multiple Choice

Solve the following system by graphing.  What is the solution?

• (3, -1)
• (-1, -3)
• (-1, -1)
• (-1, 3)

Multiple Choice

Solve the following system by graphing.  What is the solution?

• (-4, 2)
• (4, 2)
• (2, -4)
• (2, 4)

Multiple Choice

Solve this system of equations by graphing.

y = 1/2x + 2

y = -3x + 9

• (2, 3)

• (-2, -3)

• (3, 2)

• (-3, 2)