Solving by Graphing
y = 2
y = -2x - 4
(-3, 2)
y = 3x
2y - 5x = 4
(4, 12)
x - 2y = -10
-x - 2y = -14
(2, 6)
What method would be best to solve? Solve the system
x + y = 1
2x + 4y = 0
Substitution or elimination(Could argue for both)
(2, -1)
The sum of two numbers is 14. Their difference is 2. Find the numbers.
The numbers are 6 and 8
y = -x + 4
y = 5/3x - 4
(3, 1)
y = -4x - 1
y = -2x + 1
(-1, 3)
-5x - 4y = 11
-2x + 4y = 10
(-3, 1)
What method would be best to solve? Solve the system
y = 3x - 1
y = -2x + 4
Substitution or graphing(Could argue for both)
(1, 2)
Mrs. Frazier ordered lunch for herself and several (of her fabulous math) coworkers on Monday and Tuesday. On Monday, she paid $7 for five sandwiches and four sodas. On Tuesday, she paid $6 for four of each. Find the price of each item
$1 per sandwich
$0.50 per soda
y = 3/2x - 3
y = -1/6x + 7
(6, 6)
6x - 2y = -16
x - 2y = 9
(-5, -7)
-14x + 8y = 14
-7x + 6y = 21
(3, 7)
What method would be best to solve? Solve the system
-11x - 5y = -11
-x - 3y = -1
Elimination
(1, 0)
Emily's school is selling tickets to a choral performance. On the first day of ticket sales the school sold 8 adult tickets and 3 child tickets for a total of $136. The school took in $124 on the second day by selling 2 adult tickets and 12 child tickets. Find the price of an adult ticket and the price of a child ticket.
Each adult ticket costs $14 and each child ticket costs $8
2y = x - 14
(4, -5)
-8x + 2y= - 20
3x + 6y = -6
(2, -2)
-2x - 12y = 22
-3x + 9y = 6
What method would be best to solve? Solve the system
6x - 20y = -14
-x - 10y = 29
Substitution or Elimination(Could argue for both)
(-9, -2)
Ryan and Jimmy each improved their yards by planting rose bushes and ivy. They bought their supplies from the same store. Ryan spent $176 on 10 rose bushes and 14 pots of ivy. Jimmy spent $92 on 6 rose bushes and 5 pots of ivy. What is the cost of one rose bush and the cost of one pot of ivy?
Each rose bush costs $12 and each pot of ivy costs $4
-x = 4y + 4
4y + x = -4
No Solution (Parallel lines)
-10x + 12y = 0
5x - 6y = -3
No Solution
12 + 3x = 8y
2x = 9y - 8
(-4, 0)
What method would be best to solve? Solve the system
12x + 9y = -27
4x + 3y = -9
Elimination
Infinite number of solutions(if graphed, we would have the same line)
Brenda and Mofor are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Brenda sold 9 boxes of oranges and 13 large boxes of oranges for a total of $306. Mofor sold 5 small boxes of oranges and 4 large boxes of oranges for a total of $112. Find the cost of one small box of oranges and one large box of oranges.
The cost for a small box of oranges is $8 and the cost for a large box of oranges is $18