Systems of Equations

Systems of Equations

What answer choices are possible when you draw 2 lines on the same graph?

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

Multiple Choice

Here is an example of 2 lines being graphed. What answer choice matches the situation shown?

• The liness intersect

• The lines do not intersect

• The lines are on top of each others

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

Multiple Choice

Here is an example of 2 lines being graphed. What answer choice matches the situation shown?

• The liness intersect

• The lines do not intersect

• The lines are on top of each others

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

Here is an example of 2 lines being graphed. What answer choice matches the situation shown?

• The liness intersect

• The lines do not intersect

• The lines are on top of each others

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.

Look at the next 6 questions. Determine the correct solution for each problem.

Choose the correct ordered pair as (x,y) if the lines cross once.

Choose NO SOLUTION if the lines are parallel. Choose INFINITE SOLUTIONS if the lines are on top of each other.

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

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

• (4,2)

• (-2,1)

• No Solution

• Infinite Solutions

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

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?

• (1,-1)

• (-1,-1)

• (1,1)

• (-1,1)

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 Select

Choose the graph or graphs that have one solution. Check the box or boxes that apply.

Multiple Select

Choose the graph or graphs that have INFINITE SOLUTIONS. Check the box or boxes that apply.