Systems of Equations & Direct Variation

​Systems of Equations

​Today we will learn how to solve systems of equations

​Find the solution:

​Find the solution:

Multiple Choice

Find the solution:

• (0,-1)

• (-1,-1)

• (0,0)

• (-1,0)

Multiple Choice

Find the solution:

• (0,0)

• (0,2)

• (2,0)

• (0,1.5)

Multiple Choice

After how many months will both memberships cost the same amount?

• 6

• 7

• 4

• 100

Let's Review





How do we answer questions like the one below?
(Systems of Equations)

​Direct Variation

​Today we will solve for Direct Variation by setting up a proportion and cross multiplying

Fill in the Blank

Today we will solve for Direct Variation by setting up a ___________

and ______ _________

(Rewrite the entire sentence)

​Direct Variation:

​The value of y varies directly with x.

If y=6, then x=8. What is the value of y when x=12?

​Direct Variation:

​The value of y is directly proportional to the value of x.

If x=90 when y=135, what is the value of x when y=36?

​Direct Variation:

​The shadow of an object varies directly with its height.

The shadow of a 25 foot object is 6 feet.

How long is the shadow of an 18 foot tree?

Fill in the Blank

The gallons of water a dishwasher uses varies directly to the number of loads of dishes.

If the dishwasher uses 36 gallons of water for 12 loads of dishes, how many gallons will it

use for 10 loads of dishes?

Multiple Choice

The number of bracelets Meredith can make varies directly with the amount of time spent making them. If she can make 5 bracelets in 2.5 hours, how many bracelets can she make in 6 hours?

• 12 bracelets
• 10 bracelets
• 15 bracelets
• 8 bracelets

Fill in the Blank

The cost to stay at a hotel varies directly with the number of nights a customer will stay. If a customer pays $384 for 4 nights, how much

will they pay for 5 nights?

​Let's Review:




How do we solve problems like the one below?
(Direct Variation)



The distance, d, varies directly with the time, t. If you have driven 175 miles for 5 hours, how long would you drive for 210 miles?