What are the three methods for solving a system of equations?
Substitution, Elimination, Graphing
100
Solve by Graphing.
Y=x
y=-1/2x+3
(2,2)
100
What is the 1st step of this problem?
5x-2y=-11
4x+2y=5
Eliminate -2y and 2y, add 5x+4x to get 9x
100
Write what the equations would look like after you 1st substitute for y.
y=3x+2
5x+y=9
5x+3x+2=9
100
If x+y=35 represents the number of tickets sold and 2x+3y=90 represents the ticket cost. How many adult (x) tickets and how many student (y) tickets were sold?
Adult:15 Student:20
200
What is another name for the elimination method?
Combination
200
Graph to solve
y=-x
y=2x+6
(-2,2)
200
2x+4y=1
x-4y=3
What would the equation look like once you eliminate one of the variables and combine the others?
3x=4
200
Solve by substitution
x=3y
x=y+4
y=2 x=6
(6,2)
200
Carlos bought 4 slices of cheese pizza and 9 slices of mushroom pizza for a total of $31.00. James bought 3 slices of cheese pizza and 4 slices and mushroom pizza for a total for $15.00. What is the price of cheese pizza?
$1.00 per slice
300
If two lines are parallel what type of solution would you have?
No solution
300
Solve using ANY method
y=3x-2
7y+6x=40
X=2 y=4
(2,4)
300
Solve by Elimination
10x+2y=30
-x-2y=6
x=4 y=-5
(4,-5)
300
Solve by substitution
4x+5y=40
y=x-1
x=5 y=4
(5,4)
300
Megan sold 200 tickets for the band concert. Student tickets cost $5 and adult tickets cost $10. Megans sales totaled $1,750. How many adult tickets and how many student tickets did she sell.
Adult:150 Student:50
400
What is slope-intercept form?
y = mx + b
400
Which system of equations has no solution?
A. B.
5x-8y=10 5x-8y=10
5x-8y=10 -5x+8y=10
B
400
Solve by elimination
5x+2y=8
10x+4y=16
Infinitely many solutions
400
Solve using ANY method
x=3y-6
4x+3y=6
x=0 y=2
(0,2)
400
There are 13 animals in the barn. Some are chickens and some are pigs. There are 40 legs in all. How many of each animal is there?
Pigs:7 Chickens:6
500
If you have the same line, what type of solution would you have?
infinitely many solutions
500
What is the x-coordinate of the solution of the equations x+2y=9 and x-y=3
x=5
500
Solve using ANY method
3x+y=8
2x-3y=-2
x=2 y=2
(2,2)
500
Solve using substitution
3x-2y=4
y=2x-1
x=-2 y=-5
(-2,-5)
500
The sum of two numbers is 104. Their difference is 68. What are the numbers?