Random
Graphing
Substitution
Elimination
Word Problems
100
To solve a system of equations by graphing, what form must the equations be in?
Slope-intercept
100
Solve Using Graphing:
y = -3
y = 5/3x -3
(0,-3)
100
What are 3 methods of solving systems of equations?
elimination
graphing
substitution
100
The method of solving equations where you add or subtract equations to end up with one variable.
elimination
100
A local coffee shop sells small coffees for $2 and large coffees for $4. On Tuesday morning, they sold a total of 45 coffees and made $130.
Write a system of equations to find how many small coffees (s) and how many large coffees (l) were sold.
2s+4l=130
s+l=45
200
What is the first step when solving a system of equations by substitution?
solve for x or y
200
How many solutions for the following system of equations?
one
200
Solve the systems of equations using substitution
x=-3
x - 3y=-15
(-3,4)
200
Use ELIMINATION to solve each system of equations.
-3x + 2y = 23
-5x - 2y = 17
(-5, 4)
200
Gym A charges a one-time sign-up fee of $50 and a monthly fee of $20. Gym B has no sign-up fee but charges a monthly fee of $30.
After how many months will the total cost for either gyms be exactly the same?
5 months
300
What is the first step when solving systems of equations by elimination?
Equations must be lined up the same. In the same order.
300
What is the solution?
(-1,1)
300
Solve the systems of equations using substitution:
y = 6x
2x + 3y=-20
(-1,-6)
300
Use ELIMINATION to solve each system of equations.
-4x + 7y =-13
4x - 7y =3
no solution
300
A community theater sells adult tickets for $15 each and student tickets for $10 each. For the Saturday matinee, the theater sold a total of 120 tickets and brought in $1,450 in revenue.
Find the exact number of adult tickets and student tickets sold.
The theater sold 50 adult tickets and 70 student tickets.
400
What is the last step when solving by any of the 3 methods.
Substitution
400
How many solutions are there?
No Solutions
400
Solve the systems of equations using substitution:
x=4y
x+2y=12
(8,2)
400
Use ELIMINATION to solve each system of equations.
8x+ 12y = 20
-8x - 12y = -20
infinite solutions
400
A kayaker paddles 12 miles downstream (with the current) in 2 hours. On the return trip paddling upstream (against the same current), the journey takes them 4 hours.
Determine the kayaker's paddling speed in still water (x) and the speed of the river's current (y) in miles per hour.
(Hint: Distance= Rate X Time)
The kayaker's paddling speed is 4.5 mph and the river current is 1.5 mph.
500
When using the substitution method, what would be the first step when solving for x in the first equation?
5x +5y = 10
8x + 4y = 0
Subtract the 5y
500
How many solutions are there?
Infinitely Many Solutions
500
Use substitution to solve the following system of equations.
y = -2x + 3
8x + 4y =12
infinitely many solutions
500
Use ELIMINATION to solve each system of equations.
x + y = 4
2x - 5y = 15
(5,-1)
500
A chemist needs to create 10 liters of a 32% acid solution for an experiment. In the lab, they only have access to two stock bottles: a 20% acid solution and a 50% acid solution.
Set up and solve a system of equations to figure out how many liters of the 20% solution and how many liters of the 50% solution must be mixed together to get the desired result. (Hint: how many liters of acid are needed?)
The chemist needs 6 liters of the 20% solution and 4 liters of the 50% solution.