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Writing Systems of Equations

Multiple Choice

How many solutions will this system have? 

• No solution
• One Solution
• I Don't Know
• Infinitely Many Solutions

Multiple Choice

How many solutions will this system have?

• One
• Two
• No Solution
• Infinitely Many Solutions

Multiple Choice

How many solutions will this system have?

• No Solution
• Infinitely Many Solutions
• No Clue
• One solution

Multiple Choice

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

Multiple Choice

If a system of linear equations has infinitely many solutions, what does this mean about the two lines? 

• Intersecting lines
• Same line
• Parallel lines

y=

[y=][enter equations][graph][2nd][trace][5][enter x3]

Multiple Choice

Solve by graphing.
y = 2x + 1
y = 4x - 1

• (1,3)
• (-1,-3)
• (-1,3)
• (3,1)

Multiple Choice

Solve for x and y.
y = 2/3x - 2
y = -x + 3

• (0,3)
• (0,-3)
• (3,0)
• (-3,0)

Matrix

[2nd][matrix][edit][input numbers][2nd][mode][2nd][matrix][math][b][2nd][matrix][enter x2]

Multiple Choice

Solve the system of equations.

-x + y = -13

-8x - 4y = -8

• (5, 8)

• (5, -8)

• (-5, -18)

• (-5, 8)

Multiple Choice

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)

Multiple Choice

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6
• x + y = 4
  x - y = 6
• 4x + 6y = 13
  3x + 7y = 13.5
• 4x - 6y = 13
  3x - 7y = 13.5

Multiple Choice

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450
• 3x + 2y = 450
  2x + 4y = 315
• 2x + 2y = 315
  3x + 4y = 450

Multiple Choice

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  How long does it take her to do a haircut?
3x + 2y = 315
2x + 4y = 450

• 45 minutes
• 90 minutes

• 60 minutes

• 30 minutes

Multiple Choice

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

• Sugar Cookies $5 
  Oatmeal Cookies $3
• Sugar Cookies $4
  Oatmeal Cookies $8
• Sugar Cookies $2
  Oatmeal Cookies $6
• Sugar Cookies $3
  Oatmeal Cookies $6

Multiple Choice

The senior class at Rivermont High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Washington High School rented and filled 12 vans and 14 buses with 770 students. How many students were on each van and each bus?

• Van 43
  Bus 14
• Van 11
  Bus 21
• Van 14
  Bus 43
• Van 17
  Bus 45

Multiple Choice

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• (35, 52)
• (18, 69)
• ( 52, 35) 
• (61, 26)

Multiple Choice

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?

• x + y = 15
  4x + 2y = 44
• 4x + 2y = 15
  x + y = 44
• x = 2y + 44
  4x = y + 15
• 2x - 4y = 44
  x - y = 15

Open Ended

Exit Ticket-

Explain how you would write the equations in standard form AX+BY=C.

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

Multiple Choice

Solve this system by substitution.

• (1, -4)

• (1, 4)

• (-4, -7)

• (-7, -4)

Multiple Choice

What is the solution to this system of equations?

• (4, -1)
• (-1, 4)
• (-4, 1)
• (-4, -1)

Multiple Choice

The first step in solving using the substitution method is __________.

• get x by itself
• get y by itself
• get either variable by itself
• add the equations together

Multiple Choice

How many solutions will this system have? 

• No solution
• One Solution
• I Don't Know
• Infinitely Many Solutions

Multiple Choice

Solve by matrices.

4x+9y=28

-4x-y=-28

• (-7,0)

• (6,0)

• (-6,0)

• (7,0)

Multiple Choice

Solve by matrices.

7x+y=-9

-3x-y=5

• No solution

• (1,8)

• (-2,-3)

• (-1,-2)

Multiple Choice

What is the first step in solving a system of equations by elimination/matrices?

• Get both equations in standard form and line up the like terms.

• Get both equations in slope-intercept form.

• Get both equations equal to zero.

• Put the x terms first.

Multiple Choice

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph
• Don't touch
• Intersect
• Exist

Multiple Choice

3x + y = –14

–2x – y = 9

Which method would be best for solving this system?

• Substitution

• Elimination/Matrices

Multiple Choice

Which is the best method to use?

y = 6x − 11

−2x − 3y = −7

• Graphing

• Substitution because a variable is isolated.

• Elimination because both equations are in standard form.

Multiple Choice

Solve for x and y.
y = 2/3x - 2
y = -x + 3

• (0,3)
• (0,-3)
• (3,0)
• (-3,0)

Multiple Choice

Is (1,10) a solution to

y=7x+5

y=x+9

• yes

• no

Multiple Choice

Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)
• (-2,-5)
• (2,-5)
• (2,5)

Multiple Choice

What is the value of the y-coordinate of the solution to the system of equations 
x-2y=1
x+4y=7 

• 1
• -1
• 3
• 4

Multiple Choice

Solve the following systems of equations using substitution:

2y + x = -15

x = 3y

• (-3, -9)

• (-9, -3)

• (-3, 9)

• (9, -3)

Multiple Choice

This graph matches which inequality?

• y > 3
• y ≥ 3
• x≥3
• x>3

Multiple Choice

Given the system, determine a solution.

• No solution
• Infinite solutions
• (-5, 5)
• (5, -5)

Multiple Choice

Select the graph for 5x+ y ≤  -1 .

• A
• B
• C
• D

Multiple Choice

Which system of linear inequalities is represented by the graph?

• y≤2x-1
  y>-2x+3
• y>2x-1
  y≤-2x+3
• y<2x-1
  y≥-2x+3
• y≤2x-1
  y>2x+3

Multiple Choice

Solve the system of inequalities by graphing.

Multiple Choice

Which inequality describes this graph...

• y < 3x - 2

• y > 3x + 2

• y < 3x + 2

• y > 3x -2

Multiple Choice

Which of the following equations match the given graph?

• y ≥ 2/5x + 1
• y ≥ -2/5x + 1
• y≤  2/5x + 1
• y ≥ -2/5x - 1

Multiple Choice

If the inequality symbol is  $$\le$$   or  $$\ge$$ , the line will be  ___________.

• solid

• dotted

Multiple Choice

If the inequality symbol is  $$<$$  or  $$>$$ , the line will be _________.

• solid

• dotted

Multiple Choice

If the inequality symbol is  $$>$$  or  $$\ge$$  you shade ________.

• above

• below

Multiple Choice

If the inequality symbol is  $$<$$  or  $$\le$$   you shade ________.

• above

• below

Multiple Choice

Which of the following inequalities matches the given graph?

• x ≥ -1
• x ≤ -1
• x > -1
• x < -1

Multiple Choice

^{Which point is a solution to the system of inequalities?}

• (-8,2)

• (-2,-5)

• (0,6)

• (4, 3)

Multiple Choice

Which point below is NOT part of the solution set?

• (0, 0)
• (5, 1)
• (-1, -3)
• (20, -5)

Multiple Choice

Which inequality is shown in the graph?

• y < 2x + 1
• y < -2x + 1
• y ≤ 2x + 1
• y ≤ -2x + 1

Multiple Choice

Which system of inequalities is shown?

• y ≥ -x - 1
  y < x + 4
• y < -x - 1
   y ≥ x + 4
• y > -x - 1
  y ≥ x + 4
• y > -x - 1
  y ≥ x + 3

Multiple Choice

Match

• y < x−2 
  y < 3
• y > -x+2
  y > 3
• y < -x+2
  y < 3
• y < -x+2
  y > 3

Multiple Choice

When graphed, the line will be...

5 ≥ x

• Solid

• Dashed

• Zig-Zag

Multiple Choice

Which system of inequalities matches the graph?

• y > 2x - 4
  y < 2
• y < 2x - 4
  y < 2
• y > 2x - 4
  y <  2 
• y < 2x - 4
  y <   -2

Multiple Choice

Solve the system of inequalities by graphing.