System of Equations and Their Graphs

How many solutions does the following system have? Why?
y = -2/3x + 5
2x + 3y = 15

• None.  The equations have the same slope and different  
  y-intercepts

• Infinitely many.  The equations are exactly the same when in slope-intercept form.

• Three.  There are two equations so there are exactly three solutions to the system.

• One.  The equations have different slopes so there is exactly one solution.

Tags

CCSS.8.EE.C.8B

What is the solution to the set of equations?
y = -x - 2
y = -5x + 2

•   (3, 1)

•   (1, -3)

•   (-1, -3)

•   (-3, 1)

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Is the point (2, 3) a possible solution?  Explain.

• Yes.  The point is on the graphed line.

• No.  The point is NOT on the graphed line.

Refer to number 13 on your review for the scenario for this problem.
Which graph represents the numbers of packs of Spring Mix A and Spring Mix B that can be produced each day?

• Graph A

• Graph B

• Graph C

• Graph D

Tags

CCSS.HSA.REI.D.12

Refer to number 16 on your review for the scenario for this problem. 
16. a.  Write a system of equations in terms of x and y to model the situation.
(Which set of equations best represents your answer for 16 a?)

• 2x + 3y = 20
        xy = 44

• x + y = 20
        2x + 3y = 44

• 2x + 3y = 20
        2x + 3y = 44

• x + y = 44
        3x + 2y = 20

Tags

CCSS.8.EE.C.8C

Refer to number 12 on your review for the scenario for this problem.
The inequalities are
y ≥ -.25x + 6   and  y ≤ 2/3x
If x represents weeks, after how many weeks will their sales begin to overlap?

•   After 9 weeks

•   In less than 6 weeks

•   After 2 weeks

•   In less than 7 weeks

What is the solution to the system of linear equations from the graph?

• No solution

• Infinite Solutions

• (0,1)

• (1,0)

• 1

Tags

CCSS.8.EE.C.8B

A solution to a system tells us when...

• x and y are the SAME for both equations

• x is GREATER than y on one equation

• y is GREATER than x on one equation

• x and y START on the graph

Tags

CCSS.8.EE.C.8B

Copland competes in 27 swimming events this season. He wins either first place or second place in each event. Copland has 3 more first-place wins than second-place wins. Which system of equations represents this story?

Tags

CCSS.8.EE.C.8C

There are 47 people attending a play at an outdoor theater. There are 11 groups of people sitting in groups of 3 or 5. Which system of equations best represents this story?

Tags

CCSS.HSA.CED.A.3