Substitution/Elimination
Cramer's Rule
Random Systems
Setting up Word Problems
Graphing inequalities
100
Solve using Elimination:
3x-4y=5 2x+4y=10
(3, 1)
100
Solve Using Cramer's Rule:
x+3y=6 2x-y=12
(6,0)
100
Solve using any method:
x-y=10 6x+3y=6
(4, -6)
100
Andrew bought 45 apples from the apple orchard. He bought 12 more Honey Crisps than Granny Smiths.
SET UP THE EQUATIONS (you do not have to solve)
H+G=45
H=G+12
100
Graph and shade:
y-3x>-6
Shade above (m=3 and y int -6)
200
Solve Using Substitution:
x+3y=6 2x-y=12
(6,0)
200
Solve Using Cramer's Rule: (you may get fractions)
4x+2y=9
3x-y=8
(2.5, -0.5)
200
Solve using any method:
3x-4y=2 y=2x-8
(6,4)
200
Ali bought paintbrushes at two different stores. At Michael's she bought some small paintbrushes which cost $2 and some large paint brushes which cost $5. The total cost was $28. At JoAnn Fabrics she bought the same amount of small brushes but they cost $2.50 each and the same amount of large brushes which cost $4.80 each. The total cost at JoAnn Fabrics was $32.30.
SET UP THE EQUATIONS TO SOLVE FOR THE NUMBER OF BRUSHES BOUGHT (You do NOT need to solve)
2S+5L=28
2.5S+4.8L=32.30
200
Graph and shade:
|x|<6
Shade in between 2 vertical lines x=-6 and x=6
300
Solve using Substitution:
4x-3y=11 3x-6y=12
(2,-1)
300
Solve Using Cramer's Rule:
3x=1+2y 2x-3y=9
(-3,-5)
300
Solve using any method:
2y-4x=-20 y+10=2x
Infinite Solutions
300
Billy’s Restaurant ordered 200 flowers for Mother’s Day. They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each. They ordered mostly carnations, and 20 fewer roses than daisies. The total order came to $589.50.
SET UP THE EQUATIONS (you do not have to solve)
C+R+D=200
1.5C+5.75R+2.6D=589.50
D-20=R
300
Graph and Shade:
y>|x-2|+6
8x-4y<4
Shade Above (vertex (2,6)) and above (m=-2 y int -1)
400
Solve Using Elimination:
-7y=14-3x 12x=5y+10
(0, -2)
400
Solve Using Cramer's Rule:
3x-4y=5 9x=15+12y
Infinite Solutions
400
Solve:
9x-12y=10 4y=-5+3x
No solution
400
Joseph ordered 40 bags of chips for his birthday that cost $415.30. The barbeque chips bags cost $3.50 a piece, the salt and vinegar chips cost $2.30 a piece, and the lime chips cost $3 a piece. He bought 3 times as many barbeque chips as he did lime chips.
SET UP THE EQUATIONS (you do not have to solve)
B+V+L=40
3.5B+2.3V+3L=415.30
3L=B
400
Graph and Shade:
3y< x+3
2x-3y<12
Shade below (m=1/3 y int=1) shade above (m=2/3 y int: -4)
500
Solve:
(2, -1, -4)
500
Solve:
(-3, 2, -1)
500
Solve:
2x-4y+3z=0
x-2y-5z=13
5x+3y-2z=19
(3,0,-2)
500
Grant filled his bucket with 115 pieces of candy on Halloween which weighed 21.6 pounds. He is picky so he only collected KitKat bars, Nerds, and Sour Patch Kids. He ended up with mostly Sour Patch kids, and 16 more KitKats than Nerds. Each KitKat weighs .6 pounds, the Nerds box weighs 1.8 pounds, and the Sour Patch Kids pack weighs about 1.2 pounds.
SET UP THE EQUATIONS (you do NOT need to solve)
K+N+P=115
16+N=K
.6K+1.8N+1.2P=21.6
500
Graph and Shade:
y>5
2y<6x
y>3|x-4|-1
1. above horz line
2. Right m=3 yint 0
3. Inside a= 3 V: (4, -1)
(OVERLAP = rect between line #2 and right side of V)