Systems of Equations

Multiple Select

Select all that apply to the y-intercept.

• Whenever x is 0.

• Initial value

• Rate of change

• Point on the y-axis.

Fill in the Blank

For the test problem, Gilda found the y-intercept of -215 and Kalel found a slope of -2. Use both values to write this equation in slope-intercept form.

=

-

-

Fill in the Blank

Daniel booked the photographer for $125 for an upcoming event. The day of the event, the photographer charged an additional $195 per hour. What is the total price Daniel had to pay the photographer for 4 hours of service?

System of Equations

Two or more equations with the same variable.
For ex:
^{-3x+y=2
x+y=6}

​Two or more lines on a graph with (x,y) values.

System 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 (parallel)

• 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 lines intersect

• The lines do not intersect

• The lines are on top of each other

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 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 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 set of 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

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

Multiple Choice

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

Multiple Choice

Select the lesson we have NOT discussed at all.

• Solve Multistep equations

  (isolating the variable)

• Write and graph linear equations

• Operations with scientific notation

• Use powers of 10 to Estimate Quantities.

• Construct Functions to Model

Poll

Are you understanding this lesson on systems of equations?

• Yes