Systems with Graphs
Solving by Substitution
Solving by Elimination
Best Strategy
Word Problems
100
What is the solution?
(-1,1)
100
Solve the systems of equations:
-3x + 4y = -2
y = -5
(-6, -5)
100
Solve the systems of equations:
14x + 2y = 26
-14x - 6y = -50
(1, 6)
100
What strategy would be best?
14x + 2y = 26
-14x - 6y = -50
Elimination because the coefficients on x are the same number with opposite signs
100
Find the value of two numbers if their sum is 125 and their difference is 19.
53 and 72
200
Solve using Graphing
y= 2x + 1
y= -x + 7
(2, 5)
200
Solve the systems of equations:
-5x - 5y = 10
y = -4x -17
(-5, 3)
200
Solve the systems of equations:
x -3y = 6
x + 3y = 12
(9,1)
200
What strategy would be best?
y = 4x + 3
y = -2x + 1
Graphing because both equations are in slope-intercept form
200
Traveling with the current a certain boat went 25 mph. Against the same current it only went 5 mph. Find the current and the speed of the boat if there were no current.
Boat: 15 mph, Current: 10 mph
300
Solve Using Graphing:
y = 5/3x + 2
y = -3
300
Solve the systems of equations:
y = -2x - 9
3x -6y = 9
(-3, -3)
300
Solve the systems of equations:
-6x - 10y = 4
6x + 10y = 0
No Solution
300
What strategy would be best?
x = 3y + 4
5x + 2y = 12
Substitution because one of the equations is already solved for a variable
300
Shawna and Johnny are selling flower bulbs for a school fundraiser. Customers can buy packages of tulip bulbs and bags of daffodil bulbs. Shawna sold 8 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $140. Johnny sold 8 packages of tulip bulbs and 20 bags of daffodil bulbs for a total of $212. Find the cost each of one package of tulips bulbs and one bag of daffodil bulbs.
package of tulips bulbs: $4, bag of daffodil bulbs: $9
400
How many solutions are there?
Infinitely Many Solutions
400
Solve the systems of equations:
-8x - 5y = -24
-x + y = 10
(-2, 8)
400
Solve the systems of equations:
-3x - 24y = -66
3x + 4y = -14
(-10, 4)
400
What strategy would be best?
3x - 4y = 12
2x + 2y = 6
Elimination Method or Graphing using intercepts
400
Dominic's school is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 13 adult tickets and 16 child tickets for a total of $374. The school took in $304 on the second day by selling 8 adult tickets and 16 child tickets. What is the price each of one adult ticket and one child ticket?
adult ticket: $14, child ticket: $12
500
Solve the systems of linear equations by graphing:
500
Solve the systems of equations:
-8x + y = -7
16x - 2y = 14
Infinitely Many Solutions
500
Solve the systems of equations:
-15x + 6y = -36
4x - 3y = 11
(2, -1)
500
What method would be the best?
3y = 6 - 4x
4y = 3x + 8
Graphing
500
The indoor climbing gym is a popular field trip destination. This year the senior class at Prairie View and the senior class at Osawatomie both planned trips there. The senior class at Prairie View rented and filled 5 vans and 10 buses with 260 students. Osawatomie rented and filled 15 vans and 10 buses with 360 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
van: 10, bus: 21