Solving Systems of Equations
Solving Systems of Equations
Word Problems
Miscellaneous
Graphs
100
x-y=1
y=5
(6,5)
100
2x+y=8
x=5
(5,-2)
100
You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?
x=# of hot dogs sold
y=# of sodas sold
1.50x+0.50y=78.50
x+y=87
100
A system of equations makes parallel lines. How many solutions are there?
No solution
100
How many solutions does the graph have?
No solution/0
200
x-y=7
x-y=-4
No solution
200
y=2/3x-1
y=-x+4
(3,1)
200
Nolan is going to a carnival that has games and rides. Each game costs $2.50 and each ride costs $3.50. Nolan spent $52.50 altogether on 17 games and rides. Write a system of equations that could be used to determine the number of games Nolan played and the number of rides Nolan went on. Define the variables that you use to write the system.
x=# of games
y=# of rides
2.50x+3.50y=52.50
x+y=17
200
True or false: For systems of equations, the solutions are the intersections of lines.
True
200
How many solutions does this graph have?
1 solution
300
y=x-1
x+4y=16
(4,3)
300
5x+2y=4
9x+2y=12
(2,-3)
300
Parker owns a food truck that sells tacos and burritos. He sells each taco for $4.50 and each burrito for $6.75. Yesterday Parker made a total of $576 in revenue from all burrito and taco sales and there were twice as many burritos sold as there were tacos sold. Write a system of equations that could be used to determine the number of tacos sold and the number of burritos sold. Define the variables that you use to write the system.
x=# of tacos sold
y=# of burritos sold
4.50x+6.75y=576
y=2x
300
What are the 3 types of solutions to systems of equations?
Infinitely many solutions, no solution, or an ordered pair.
300
How many solutions does this graph have?
Infinitely Many Solutions
400
x+2y=4
y=-1/2x+2
Infinite Solutions
400
3x-2y=-16
x+y=-7
(-6,-1)
400
A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 12 granola bars and each large box has 18 granola bars. The camp bought a total of 15 boxes that have 240 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
x=# of small boxes purchased
y=# of large boxes purchased
12x+18y=240
x+y=15
400
What is a system of equations?
Two or more equations that are graphed on the same coordinate plane.
400
What is the solution to the graph?
(-4,5)
500
5x+4y=-12
3x-4y=-20
(-4,2)
500
y=-2x-1
3x-4y=-40
(-4,7)
500
Isaac owns a trucking company. For every truck that goes out, Isaac must pay the driver $19 per hour of driving and also has an expense of $1.50 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 30 miles per hour and Isaac's total expenses for the driver, gas and truck maintenance were $512. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system.
x=# of hours the driver drove
y=the # of miles driven
19x+1.50y=512
y=30x
500
A system of equations produces lines that overlap. How many solutions are there?
Infinitely many solutions.
500
What is the solution to the graph?
(-6,2)