G8.M6.Review - System of Equations

Draw

For each ordered pair, determine whether it is a solution to the system of equations:

$$-3x+2y=5$$

$$2x-7y=8$$

Multiple Choice

For the shown system of equation, choose the best description of its solution.

If the system has exactly one solution, give its solution.

• The system has infinitely many solutions.

• The system has no solution.

• The system has exactly one solution.

Multiple Choice

For the shown system of equation, choose the best description of its solution.

If the system has exactly one solution, give its solution.

• The system has infinitely many solutions.

• The system has no solution.

• The system has exactly one solution.

Multiple Choice

For the shown system of equation, choose the best description of its solution.

If the system has exactly one solution, give its solution.

• The system has infinitely many solutions.

• The system has no solution.

• The system has exactly one solution.

​A solution to a system of linear equations is a point where the lines intersect. There are three possibilities.

↦Exactly one solution: This occurs when the lines intersect at a single point.
↦Infinitely many solutions: 

This occurs when the two lines

are the same.
↦No solution: This occurs when

the two lines are different and

parallel.

Let's look at the systems of

equations we were given.

Draw

Here is a system of equations.

y=-3x+4

y=-3x+3

Graph the system. Then write its solution.

Note that you can also answer "No solution" or "Infinitely many" solutions.

​​A solution to a system of linear equations is a point where the lines intersect. There are three possibilities.

↦Exactly one solution: This occurs when the lines intersect at a single point.
↦Infinitely many solutions: This occurs when the two lines are the same.
↦No solution: This occurs when the two lines are different and parallel.

Draw

Graph the system below and write its solution.

−4x-2y=-2

y=-2x+3

Open Ended

Solve the system of equations:

$$y=2x+56$$

$$y=9x$$

Multiple Choice

Solve the following system of equations

-5x+2y=6

10x-2y=-16

• (-2,2)

• (2,2)

• (-2,-2)

• (2,-2)

Multiple Choice

For the system

3x+5y=11

2x+5y=4

, choose the best description of its solution.

• The system has infinitely many solutions.

• The system has a unique solution.

• The system has no solution.

Open Ended

A textbook store sold a combined total of 

390

 biology and math textbooks in a week. The number of biology textbooks sold was two times the number of math textbooks sold.

How many textbooks of each type were sold?

Open Ended

One month Charlie rented 12 movies and 2 video games for a total of $29.

The next month he rented 3 movies and 5 video games for a total of $32.

Find the rental cost for each movie and each video game.

Open Ended

A store is having a sale on jelly beans and trail mix today. The table below shows the amount of each type of food (in pounds) and the total cost (in dollars) of two purchases today.

Write a system of equations that could be used to find the cost (in dollars) for each pound of jelly beans and each pound of trail mix.=+xy

Open Ended

A store is having a sale on jelly beans and trail mix today. The table below shows the amount of each type of food (in pounds) and the total cost (in dollars) of two purchases today.

How much does each pound of jelly beans and each pound of trail mix cost (in dollars)?

Open Ended

The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $1757 to rent trucks plus an additional fee of $125.25 for each ton of sugar.

The second company does not charge to rent trucks but charges $250.75 for each ton of sugar.

For what amount of sugar do the two companies charge the same?

Open Ended

The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $1757 to rent trucks plus an additional fee of $125.25 for each ton of sugar.

The second company does not charge to rent trucks but charges $250.75 for each ton of sugar.

What is the cost when the two companies charge the same?

Open Ended

Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $60. For one performance, 40 advance tickets and 20 same-day tickets were sold. The total amount paid for the tickets was $1900. 

What was the price of each kind of ticket?