Systems Overview
A system of equations has at least how many equations?
Two
If two linear equations never intersect (are parallel), how many solutions do they have?
None.
What do you need to find first when solving a system by substitution?
An isolated variable.
That one of the variables will be eliminated.
or
You have opposite variables.
You begin with $90 in your savings account and your friend begins with $35 in her savings account. You deposit $10 in savings each week, and your friend deposits $15 in savings each week.
y = 10x + 90
y = 15x +35
The name of the three methods that can be used to solve systems.
Graphing, Substitution, and Elimination.
If two linear equations lie on top of one another, how many solutions do they have?
Infinite
Solve using substitution:
2y - 3x = 15
x = 5
(5,15)
Solve using elimination:
3x + 2y = 9
2x - 2y = 6
(3, 0)
You hiking at a rate of 2 miles per hour and are already 3 miles into the trail. Someone else just started and is walking 3 miles per hour.
y = 2x + 3
y = 3x
When given a system of equations, our goal is to find the _________.
solution
If two linear equations have an intersection, how many solutions do they have?
One
Solve using substitution:
2y + 5x = 11
y = 3x
(1, 3)
Solve using elimination:
5x - 3y = 20
5x + 2y = 45
(7,5)
You sell bracelets for $2 each and necklaces for $3 each at a local flea market. You collect $95, selling a total of 37 jewelry items. How many of each type of jewelry did you sell?
2x + 3y = 95
x + y = 37
Is the following coordinate a solution to the system?
(1,3)
4x-1=y
2y+3x=9
Yes
Solve by graphing:
y=x-1
y=-x+3
(2,1)
Solve using substitution:
x = 4y - 3
2y - x = 7
(-11, -2)
Solve using elimination:
6x - 3y = 12
2x + 6y = -38
(-1,-6)
A biology test is worth 100 points and has 36 questions. Multiple-choice questions are worth 2 points each and essay questions are worth 6 points each.
x + y = 36
2x + 6y = 100
Is the following coordinate a solution to the system?
(0,-4)
y=x-4
8x-3y=7
No
Solve by graphing
y = 4x - 3
y = 4x
No solutions
Solve using substitution:
y = 3x - 5
y = -2x + 10
(3,4)
Solve using elimination:
4x - 7y = 32
-6x + 2y = -14
(1, -4)
You and your friend are buying throw blankets with your names embroidered on them. The cost of the throw blanket is x dollars and the cost of each embroidered letter is y dollars. Your name has 6 letters and the total cost is $29. Your friend's name has 3 letters and the total cost is $24.50.
x + 6y = 29
x + 3y = 24.50