Algebra 1 System of Equations

What is the solution?

• One Solution

• No solution

• Infinitely Many Solutions

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all.  Upon completing the job he counted out the coins and it came to $6.60.  Which system of equations could be used to find the exact number of dimes and nickels? 

• d + n = 6.60
  .10d + .05n = 80

• d + n = 80
  d + n = 6.60

• d + n = 80
  .10d + .05n = 6.60

• d + n = 80
  .05d + .10n = 6.60

Lisa and Tammy are selling items at the craft show.  Which might be a reasonable solution from the graph showing the number of items sold when they both have earned the same amount?

• (1, 12)

• (3, 19)

• (5, 25)

• (0, 10)

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used?

• 1s + 3c = 38
  2s + 3c = 52

• 3s + 1c = 38
  3s + 2c = 52

• s + c = 38
  s + c = 52

• 3s + 3c = 38
  1s + 2c = 52

Solve:
y = 7x + 9
2y + 2x = -18

• (5, 0)

• (9, 18)

• (-2, -5)

• (1, 16)

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

The solution to a system of equations is any ordered pair that makes both equations true. 

• TRUE

• FALSE

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

What is the solution to this equation?

• one solution

• no solution

• infinite solutions

• none of these

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative