How Many Solutions
1/2x - 5y = 10
-1/2x + 5y = -10
Infinite
y = x + 3
3x - 4y = -7
Substitution
y = 2x - 2
y = x + 3
y = 8
x = 5
3x - 8y = 31
7x +8y = 19
y = -2
x = 5
Calvin has 17 more nickels than quarters. He has 3 Quarters. How many nickels does he have?
20 nickels
x + 6y = -18
x - 6y = 18
one solution
-8x + 4y = 11
4x - y = 2
Elimination
x = 7y + 4
x = 5y - 8
y = -6
x = -38
y - 2x = 0
3y - 5x = -4
x = -4
y = -8
Bha'seers grade is half as much as Hossans. Hossan has an 80% in a class worth 100 points. How many points does Bha'seer have?
40 points
7x + 2y = -14
-7x + 2y = -14
one solution
4x + 2y = 8
7x +8y = 5
Elimination
y = 1/2x + 5
2y + 4x = -10
y = 3
x = -4
x + 6y = -18
x - 6y = 18
x = 0
y = 3
Pedro has a stand where he sells tea and lemonade. He sells lemonade for $2 per cup and tea for $4 per cup. This weekend, Pedro sold 5 times as much lemonade as tea. He earned a total of $120. Write a system of equations that represents this situation.
4t +2l = 120
l = 5t
y = 2x +4
y = 2x +9
no solutions
-5y - 12 = x
4 - 5y = x
Substitution
2x = 4y - 6
8y + 10 = 2x
y = -4
x = -9
-3x -4y = 15
9x +7y = 25
y = -14
x = 13 2/3
Maria and Curtis both study a second language. Maria studies German 3 hours per week and Curtis studies French 2 hours per week. Curtis has already studied 4 hours when Maria starts her studying. How many weeks will it take for both of them to study the same number of hours?
4 weeks.
3/4x - 9y = 12
-3/4x + 9y = 12
no solutions
2x = 5y - 3
2x = 8y + 6
Substitution
4x + y = 3
-6x - 5y = 6
y = -3
x = 3/2
x + y = 10
6x + 8y = 72
y = 6
x = 4
Agnes has 23 collectible stones, all of which are labradorite crystals or galena crystals. Labradorite crystals are worth $20 each, while galena crystals are worth $13 each. Agnes earns $439 by selling all of her crystals. How many stones of each type did she sell?
g = 3
L = 20