Analyze Systems of Equations

If a system of linear equations has an infinite number of solutions, what do you know about the graph of the system?

• The lines intersect at one point.

• The lines are parallel.

• The lines are the same line.

• The lines cannot be graphed.

The total cost, c, of belonging to two different gyms for m months is shown on the graph. The lines intersect at the point (4, 250). What does the solution means in this situation?

• At 250 months, the cost for each gym is $4

• At 4 months, the cost for each gym is $250

• 250 people get 4 months of membership for free

• 4 people get 250 months of membership for free

Use substitution to solve the system of equations. How many solutions are there?

• There are no solutions.

• There is one solution.

• There are infinitely many solutions.

• It is not possible to determine the number of solutions.

Use substitution to solve the system of equations.

y = 4.5x + 7.5

y = –3.5x – 4.5

• x = –1.5, y = –0.75

• x = 1.5, y = 0.75

• x = –1.5, y = 0.75

• x = 1.5, y = –0.75

Tickets to a school play cost $3 for students and $8 for adults. On opening night, $1,000 was collected and 150 tickets sold. Use substitution to solve a system of equations to find how many of each kind of ticket were sold?

• 40 student tickets

  110 adult tickets

• 110 student tickets

  40 adult tickets

• 50 student tickets

  100 adult tickets

• 100 student tickets

  50 adult tickets

Solve this system of equations
y=8x-5
y=2x+19

• (1,3)

• (2.4, 23.8)

• (2.5,15)

• (4,27)

Solve this system of equations
2x+y=9
y=5x+2

• (1,7)

• (2,5)

• (-1,-3)

• (5,-1)

Use elimination to solve the system of equations.

3x – 2y = 24

x + 2y = 48

• x = 18

  y = 15

• x = -18

  y = -15

• x = -18

  y = 15

• x = 18

  y = -15

What is the solution to the system of equations?

2x + 3y = 26

3x + 5y = 40

• x = 10, y = 2

• x = -10, y = -2

• x = -10, y = 2

• x = 10, y = -2

6x + 2y = 14
5x – 2y = 8
One way to solve this system of equations using elimination is to add the two equations to get 11x = 22. Then substitute 2 for x into either equation to get y = 1

• True

• False

• Both True and False

• I don't have a clue.