Question

Use the elimination method to solve each linear system.

1) 2x-9y=-55 and x+2y=18

2) 3x+2y=7 and 6x-6y=-6

3) 6x+10y=2 and 7x+4y=-13

4) 3x+2y=5 and x-2y=-1

Abby mixes cinnamon and nutmeg to make 25g of a spice mix. Cinnamon costs 9 cents per gram, and nutmeg costs 12.5 cent per gram. The spice mix costs 9.7 cents per gram. How much of each spice does Abby need to use?

1. huyenthanh
1) x=4, y=7
2) x=1, y=2
3) x=-3, y=2
4) x=1, y=1
word problem) 5g of nutmeg and 20g of cinnamon
Step-by-step explanation:
1)
2x-9y=-55
2(x+2y) = 2x+4y = 36
(2x+4y)-(2x-9y)=36-(-55)
13y = 91
y = 7 so x = 4
2)
2(3x+2y) = 6x+4y = 14
6x-6y=-6
(6x+4y)-(6x-6y) = 14-(-6)
10y = 20
y = 2 so x = 1
3)
2(6x+10y) = 12x+20y = 4
5(7x+4y) = 35x+20y = -65
(35x+20y) – (12x+20y) = -65-4
23x = -69
x = -3 so y = 2
4)
(3x+2y)+(x-2y) = 5+(-1)
4x = 4
x = 1 so y= 1
last)
c+n = 25
9c + 12.5n = 25*9.7 = 242.5
9(c+n) = 9*25
9c+9n=225
9c+12.5n – 9c-9n = 242.5-225
3.5n = 17.5
n = 5 so c = 20
5g of nutmeg and 20g of cinnamon