Solving Systems by Graphing
Determine how many solutions this system .
y=x+4
y=x-4
No solution
Solve using Substitution
y=x+5
3x+y=25
(5,10)
Solve using elimination
3j + 4k = 23.5
8j - 4k= 4
(2.5,4)
Solve the system of inequalities and name 1 possible solution.
x + y > 3
x - y < 4
Sample Answer: (5,5)
Graph each system and determine how many solutions it has. If it has one name it.
y=x+3
y=2x+4
Yes,
(-1,2)
Solve using Substitution
y=4x+5
2x+y=17
(2,13)
Solve using elimination
-3x-8y=-24
3x-5y = 4.5
(4,1.5)
Solve the system and name 1 solution
y < 2x + 2
2x + y > 4
Sample Answer: (4,4)
Graph each system and determine how many solutions it has. If it has one name it.
y=x+4
y=-x-4
Yes,
(-4,0)
Solve using substitution
2x+y=3
4x+4y=8
(1,1)
Solve using elimination
Seven times a number plus 3 times another number equals -1. The sum of the two numbers is -3. What are the numbers.
x+y=-3
7x+3y=-1
The two numbers are 2 and -5
Solve the system and name 1 solution.
2x < 4y + 1
4y > 2x + 3
Sample Answer: (4,6)
If x is the number of years since 2000 and y is the percent of people using travel services, the following equations represent the percent of people using travel agents and the percent using the internet to plan their trip.
Travel Agent: y=-2x+30
Internet: y=6x+41
Estimate the year that both were used equally.
1999
The sum of the measures of angles x and y is 180 degrees. The measure of x is 24 degrees greater than the measure angle of y.
Find the measure of each angle using substitution.
x+y=180
x=24+y
x=102, y= 78
Steve subscribed to 10 podcasts for a total of 340 minutes. He used his two favorite tags, Hobbies and Recreation and Soliloquies episode lasted 32 minutes. To how many of each tags did Steve subscribe to?
2 Soliloquies podcasts and 8 Hobbies and Recreation podcasts
Mr Redding is selling 20 notebooks and 50 pens per week with a goal earning of $60 per week.
a. Create a systems of inequalities to represent this situation.
b. Name one possible combination.
a. n≥20
p≥50
2.5n+1.25p≥60
b. Sample solution, (40,100)
Abheek and Viren are reading a graphic novel. Abheek already read 35 pages, and now is reading 20 pages every day. Viren already read 85 pages and now is reading 10 pages everyday. Graph the equation, and figure out how long will it be til Abheek has read more pages than Viren.
(5,135)
Abheek will have read more after 5 days
in 2000, the demand for nurses was 2,000,000 while the supply was 1,890,000. The projected demand for nurses in 2020 is 2,810,414, while the supply is only projected to be 2,001,998.
Use subsitution to determine in which year were the supply of nurses equal to the demand.
y=5599.9x+1,890,000
y= 40,520.7+2,000,000
During 1996
A staffing agency for in-home nurses and support staff places neccesary personnel at locations on a daily basis. Each payed nurse works 240 minutes per day at a dail rate of 590. Each support staff employee works 360 minutes per day at a daily rate of 120.
a. On a given day, 3000 total minutes are worked by the nurses and support staff that were placed. Write an equation represneting this. On the same day earnings for placed nurses and support staff totaled $1050. Write an equation representing this.
b. Solve the systems and interpret the solution in its context.
a. 240n+360s=3000, 90n+120s = 1050
b. (5,5) 5 nurses and 5 support staff were placed.
Ice resurfacers are used for rinks of at least 1000 square feet and up to 17000 square feet. The prices range from as little to as $10,000 to as much as $150,000 thousand.
Define the variables and create/graph your system of inequalities.
Name one possible solution
Is (15,000 , 30,000) a solution?
1000<f<17,000
10,000<p<150,000
Sample Answer: (5000, $20,000)
Yes the point is a solution