Intro to systems of equations

Introduction to Systems of Equations

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

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​Intro to systems of Equations

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?

• The lines do not intersect

• The lines are on top of each other

​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 solution shown?

• The lines are on top of each other

• The lines intersect

• The lines do not intersect

For lines to be right on top of each other.....

• 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 equal to one another for the lines to be on top of each other

Multiple Choice

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

• The lines intersect

• The lines do not 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 ordered 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?

• (-2,1)

• (7,5)

• (-3, 4)

• (5,2)

Multiple Choice

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

• No solution

• Infinite Solutions

• (5,3)

• (-9,3)

Multiple Choice

What is the point of intersection for the problem on the left

• Infinite Solutions

• (4,2)

• (-2,1)

Multiple Choice

What is the point of intersection at the left?

• (-1,-4)

• (4,1)

• (-2,7)

Multiple Choice

What is the point of intersection?

• (1,-1)

• (1,1)

• (-1,-1)

Multiple Choice

What is the point of intersection?

• (0,-3)

• (3,0)

• (1,2)

Multiple Choice

Choose the graph with one solution

Multiple Choice

Choose the graph that has an infinite amount of solutions