Graphing
Solve the system by graphing.
y = -2x - 4
y = 0.5x + 6
(-4, 4)
Solve the system using substitution.
y = 6x + 7
3x - 8y = 4
(-4/3, -1)
Solve the system using elimination.
x + y = 7
2x - y = 2
(3, 4)
What is the solution to a system of equations?
The system of equations is any ordered pair that solves all the equations in the system.
The point/points where both lines in the system cross.
Final Jeopardy Category: Word Problems
A rental company can set up 3 small tents and 1 large tent in 115 minutes. They can set up 2 small tents and 2 large tents in 130 minutes. How much time is required to set up a small tent?
Solve the system by graphing.
y = 0.5x - 2
y = 3x - 7
(2, -1)
Solve the system using substitution.
x = y + 6
x + y = 10
(8, 2)
Solve the system using elimination.
x + 2y = 4
2x - 5y = -1
(2, 1)
How many solutions can a system of equations have?
One solution, no solution, infinitely many solutions.
Final Jeopardy Answer:
25 minutes
Solve the system by graphing.
y = -x + 1
y = -x - 3
no solution
Solve the system using substitution.
y = 2x - 1
2x + 3y = -7
(-1/2, -2)
Solve the system using elimination.
x - 3y = -4
2x - 6y = 6
no solution
To solve this system using elimination, what number would you have to multiply the second equation by?
2x + 9y = 10
3x - y = 5
9
Solve the system by graphing.
y = (-2/3)x + 2
2x + 3y = 6
infinitely many solutions
Solve the system using substitution.
y - 3x = 1
6x - 2y = -2
Infinitely many solutions.
Solve the system using elimination.
2x + y = 2
x - 2y = -5
(-1/5, 12/5)
Maria solved a system of equations by graphing. When she graphed the system, she could only see one line on the coordinate plane. How many solutions does the system have?
Infinitely many solutions.
Two online stores sell jackets. One store sells jackets for $32 each and charges $15 for shipping. The other store sells jackets for $35 each and does not charge for shipping. How many jackets, x, would you need to buy for each company to charge you the same amount of money?
5 jackets
Mohamed and Dana are flying in their hot air balloons. Mohamed's hot air balloon is at an altitude of 40 meters and rises at a rate of 10 meters per minute. Dana's hot air balloon is at an altitude of 165 meters and descends at a rate of 15 meters per minute. In how many minutes will both balloons have the same altitude?
5 minutes.
4x - 3y = -9
3x + 2y = -11
(-3, -1)
Solve the system.
5x + 3y = 13
7x + 8y = -16
(8, -9)