Solving Systems of Equations by Graphing

Solving Systems of Equations

​Dr. Tom Giles

Solving Systems of Equations

Multiple Select

We can solve systems of equations by....

• Desmos

• Substitution

• Graphing

• Elimination

Systems of Equations - Substitution
- Elimination

Fill in the Blank

Solve this system of equations for x.

-3x + 4y = 29

y = 2x + 11

=

-

Multiple Choice

Solve this system of equations for y.

-3x + 4y = 29

y = 2x + 11

• y = 2

• y = 4

• y = 5

• y = 6

Multiple Choice

Solve this system of equations for y.

-3x + 4y = 2

y = 2x + 11

• y = 2

• y = 4

• y = 5

• y = 6

Open Ended

Solve the following system of equations

$$y=-3x+5$$   $$5x-4y=-3$$   What did you get for your solution, if any?

Multiple Choice

Solve the system by your method of choice.

x - 3y = -17

5x +3y = -13

• (5,4)

• (4,5)

• (4,-5)

• (-5,4)

Poll

For solving systems of linear equations, which method do you prefer?

• Graphing the lines

• Substitution

• Elimination

• Desmos

Multiple Choice

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  How many horses and chickens are in the barn?

• 7 Horses
  8 Chickens

• 8 Horses
  7 Chickens

• 6 Horses
  9 Chickens

• 9 Horses
  6 Chickens

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

The sum of Coach Taylor's and Ms. Sims' ages is 55.  The difference is 3.  
Solve:
x + y = 55
x - y = 3

• (26, 23)
• (26, 29)
• (29, 26)
• (29, 32)

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

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

The senior class at Wayne County 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

A test has twenty questions worth 100 points.  The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each.  How many multiple choice questions are on the test?

• 20 Multiple Choice
• 10 Multiple CHoice
• 15 Multiple Choice
• 5 multiple choice

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

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

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3
• x + y = 33
  x = 2y - 3
• x + y = 33
  x = 3 - 2y
• x + y = 3
  x = 33 - 2y

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

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

Last season two running backs on the WCHS football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

• x + y = 1550

  y = 4x

• x + y = 1550

  y = x + 4

• y - x = 1550

  y = 4x

• y = 1550 + x

  y = x + 4

Multiple Choice

Josh is thinking of two numbers.  Their sum is -10 and their difference is -2.  Which system of equations represents the situation?

• x - y = -10
  x + y = -2
• x = -2 
  y = 5
• x + y = -2
  x - y = -10
• x + y = -10
  x - y = -2

Multiple Choice

At the Wayne County bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54

  t = 3n + 8

• t + n = 54

  n = 3t + 8

• t + n = 54

  t = 3n - 8

• t + n = 8

  t = 3n + 54

Multiple Choice

Your family goes to Mississippi Fried for dinner. There are 6 people in your family. Some order the chicken fingers for $14.80, and some order the Deluxe Chicken Dinner for $17. If the total bill was $91, which system best represents the situation?

• x + y = 6

  14.80x + 17y = 91

• x + y = 91

  14.80x + 17y = 6

• x + y = 6

  14.80y + 17x = 91

• x + y = 91

  14.80x+ 17y = 6

Multiple Choice

Two equations were graphed on the set of axes below.  Which point is a solution to the system of equations ?

• (0,3)
• (5,0)
• (2,-3)
• (8,9)

Multiple Select

What are the solutions to the system of equations graphed below? (More then one correct answer).

• (2, 0)

• (0, 4)

• (-2,0)

• (0, -4)

• No Solution

Multiple Choice

How many solutions does this system of equations have?

• one solution

• two solutions

• no solution

• infinitely many solutions

Multiple Choice

Solve the system of equations.

• (0,-7) and (1, 6)

• (0,-7) and (1, -6)

• (0, 7) and (1, -6)

• (-7,0) and (1, -6)

Multiple Choice

How many solutions does this system of equations have?

• one solution

• two solutions

• no solutions

• All of the above

Multiple Choice

Find the solution.

• (2,3) and (3,4)
• (-3,-15) and (4,-8)
• (-3,10) and (8,4)
• (-8,3) and (-4,10)

Multiple Choice

The graph of f(x) and g(x) are shown below. How many solutions does the system of equations have?

• One

• Two

• Three

• Four

• No Solution

Multiple Choice

Determine the x-value of the solution to the system of equations.

• -2

• -1

• 1

• 2

Multiple Choice

Determine the "y" values of the solution:

y²-26=-x²

x-y=6

• 1 and 5

• -1 and 5

• -5 and -1

• 1 and -5