System of Equation by graphing

System of Equation by graphing

System of Equations

• Two or more equations that represent the constraints in the same situation form a system of equations. 

• solution to a system of equations

  A coordinate pair that makes both equations in the system true.

  On the graph, the solution is the point where the graphs intersect.

Multiple Choice

A ________________ is a set of two or more equations that have the same variables.

• solution of a system
• elimination method
• system of equations
• table

Multiple Choice

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

Multiple Choice

What is the solution to the system?

• (3, -1)

• (2, -6)

• No Solution

• (6, -2)

Multiple Choice

What is the solution to this system?

• (1, -1)

• (-1, 1)

• (0, -2)

• (2, 0)

Multiple Choice

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

Multiple Choice

How many solutions are there? peep the slope

y = 4x + 3

y = 4x - 2

• 0 parallel lines

• 1 different lines

• IMS the same line

Multiple Choice

How many solutions are there? peep the slope & y-intercept

y = -2x + 3

y = -2x + 3

• 0 parallel lines

• 1 different lines

• IMS the same line

Multiple Choice

How many solutions are there? peep the slope

y = 3x + 5

y = -3x - 2

• 0 parallel lines
  

• 1 intersecting lines

• IMS the same line

Multiple Choice

How many solutions will this system have?

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

Multiple Choice

This system has _____ solutions

• 0

• 1

• 2

• Infinitely many

Multiple Choice

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

• Parallel lines

• the same line

• Intersecting lines

Multiple Choice

A system of equations with no solution will have lines that...

• are the same

• cross in one place

• are parallel and never touch

Multiple Choice

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 (all) the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes and nickels? (Hint: How much are the coins worth?)

• d + n = 6.60

  .10d + .05n = 80

• d + n = 80

  d + n = 6.60

• d + n = 80

  .10d + .05n = 6.60

Multiple Choice

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530

  3S + 4A = 1740

• S + A = 530

  4S + 3A = 1740

• S + A = 1740

  3S + 4A = 530

• S + A = 1740

  4S + 3A = 530

Multiple Choice

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

Multiple Choice

The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.

• 5q + 2z = 1.32

  1z = 0.75

• 5q + 2z = 1.32

  3q + 1z = 0.75

• q + z = 1.32

  q + z = 0.75

• 5q + 2z = 0.75

  3q + 1z = 1.32

Multiple Choice

A sporting goods store sells left haded (x) and right handed (y) gloves. In one month, 12 gloves were sold for a total of $561. Right handed gloves cost $45 each and left handed gloves cost $52. Which system could be solved to determine the number of each type of glove sold?

• x + y = 561

  45x+52y=12

• x + y = 12

  52x+45y=561

• x + y = 12

  45x+52y=561

• x + y = 561

  52x+45y=12

Multiple Choice

Eddie is thinking of two numbers. If you triple the first number (x) and double the second number (y) the sum is 28. If you double the first number (x) and reduce it by the second number (y), the difference is 8. Write two equations that represent this situation.

• 2x + 2y = 28

  2x + y = 8

• 3x + 2y = 28

  2x - y = 8

• 3x - 2y = 28

  2x + y = 8