Solving Systems of Equation
y = x + 2
y = 2x - 1
(3,5)
Two movie tickets cost $18. One adult ticket costs $10 and one child ticket costs $8. Write and solve a system to find the cost of each ticket.
Adult ticket = $10, Child ticket = $8
Add:
(3x + 4) + (2x - 1)
(5x + 3)
x^2 + 5x + 6
((x + 2)(x + 3))
x^2 - 9 = 0
(x = 3, -3)
2x + y = 7
x - y = 2
(3, 1)
A school sold 20 tickets to a game for a total of $110. Student tickets cost $5 and adult tickets cost $7. How many of each ticket were sold?
15 student tickets and 5 adult tickets
Add:
(5a^2 + 2a) + (3a^2 - 7a)
(8a^2 - 5a)
x^2 + 7x + 12
((x + 3)(x + 4))
x^2 + 5x + 6 = 0
(x = -2, -3)
3x + 2y = 12
x + y = 5
(2, 3)
The sum of two numbers is 15. Their difference is 3. Find both numbers.
9 and 6
Add:
(2x^2 + 3x + 1) + (x^2 - 5x + 4)
(3x^2 - 2x + 5)
x^2 - x - 12
((x - 4)(x + 3))
x^2 - 7x + 10 = 0
(x = 5, 2)
4x - y = 9
2x + y = 3
(2, -1)
A store sold 12 notebooks and folders for $30. Notebooks cost $3 and folders cost $2. How many of each were sold?
6 notebooks and 6 folders
Add:
(4m^2 - 6m + 2) + (m^2 + 3m - 8)
(5m^2 - 3m - 6)
x^2 + 9x + 20
((x + 4)(x + 5))
x^2 + 2x - 15 = 0
(x = 3, -5)
x + y =-4
x−y=2
(-1,-3)
At a snack stand, 18 drinks and chips were sold for $39. Drinks cost $2 and chips cost $3. How many of each were sold?
15 drinks and 3 chips
Add:
(7p^2 + 4p - 9) + (2p^2 - 6p + 5)
(9p^2 - 2p - 4)
x^2 - 4x - 21
((x - 7)(x + 3))
2x^2 - 8x = 0
(x = 0, 4)