Level 1
3x+5y=0
2x -5y=-25
(-5,3)
8x+9y=82
2x+2y=20
(8,2)
Distribute -4
-2x+4y=-12
2x -4y=-18
No Solutions
x + y = -1
y = -x + 7
(-3,2)
Move -1x (changes to +1x)
2 Fancy and 5 Plain
28f+15p=131
f+ p=7
-2x+5y=-9
(2,-1)
8x+16y=80
8x+ 3y =41
(4,3)
Distribute -1
15x+27y=33
-15x-27y=-33
Infinite Solutions
2x+ y=3
-2x =-5y -9
(2,-1)
Move -5y (changes to +5y)
Cody worked 4 hours and Sam worked 5 hours and they made a total of $80. Later, Cody worked 4.5 hours and Sam worked 2.5 hours for a total of $65. How much do Cody and Sam make per hour?
Cody makes $10 per hour
Sam makes $8 per hour
4c + 5s =80
4.5c+2.5s =65
4x+9y=82
15x-9y=51
(7,6)
4x+3y=56
2x+ y=24
(8,8)
Distribute -3
3x + y =13
21x+7y=-3
No Solutions
2x-3y=12
x -6 = -3y
(6,0)
Move -6 AND -3y (change to +6 and +3y)
A theatre sold a total of 530 tickets for a show. Childrens tickets cost $3 each and adult tickets cost $5 each. If the theatre sold a total of $1740, how many of each type of ticket were sold?
455 children tickets
75 adult tickets
5a+3c=1740
a+ c = 530
6x -8y =36
-6x+18y=-36
(6,0)
5x-2y=4
3x+y=9
(2,3)
Distribute 2
-2x+5y=-2
4x-10y=4
Infinite Solutions
5y = 0 -3x
2x-5y=-25
(-5,3)
Move -3x (changes to +3x)
Joe worked 8 hours and Bonnie worked 10 hours and they made a total of $80. The next day, Joe worked 9 hours and Bonnie worked 5 hours for a total of $65. How much does each person make per hour?
Joe makes $5/hour
Bonnie makes $4/hour
8j+10b=80
9j+5b =65
36x+54y=450
-36x-45y=-405
(5,5)
4x+9y=82
5x -3y=17
(7,6)
Distribute 3
3x+15y=12
x+ 5y= 4
Infinite Solutions
x= 5 -9y
4x+9y=-7
(-4,1)
Move -9y (changes to +9y)
A baseball park sold 1,246 tickets. Adult tickets were $5 and kid tickets were $1. The park made $2,874.
How many adult and kid tickets were sold?
407 adult tickets
839 kid tickets
5a+1s=2874
a+ s =1,246