Solving Equations
2x + 3 = 11
x = 4
A water tank already contains 55 gallons of water when Baxter begins to fill it. Water flows into the tank at a rate of 8 gallons per minute. Write a linear equation to model this situation.
y=55+8x
Determine whether x=5 is a solution of 6x−17=16?
Not a Solution
y = 2x + 2
y = 5x - 7
(3, 8)
-2x - 5y = 16
2x - 3y = -16
(-8, 0)
-16 = 4x – 12
x = -1
A canoe rental service charges a $20 transportation fee and $30 dollars an hour to rent a canoe. Write and graph an equation representing the cost, y, of renting a canoe for x hours.
y=30x+20
Determine whether y=2 is a solution of 6y−4=5y−2
y = -2x + 7
y = -4x + 15
(4, -1)
2x - 3y = 18
5x - 3y = 9
(-3, -8)
-7f + 6 = 116 + 3f
f = -11
The store at which Andy usually shops is having a sale. Roast beef costs $4 a pound and shrimp costs $10 a pound. Write an equation to describe different possible combinations of Roast beef and shrimp that he can buy for $96.
Determine if the point (2, -1) is a solution to the equation 2x+y=3
It is a solution
y = x + 5
-2x + 7y = 20
(-3, 2)
9x + 3y = -15
-18x - 6y = 30
IMS
2d + 18 = 12 – 6(d + 7)
d = -6
It will take 20 points to make the playoffs, the hockey team coach told the players. “We get 2 points for a win and 1 point for a tie.” Let W be the number of wins and T the number of ties.
2W+1T=20
Determine if the point (-2, 3) is a solution to the system of equations. Explain why or why not.
2x+y=-1 and 3x-5y=7
Not a solution because it is only a solution to one equation.
y = -2x + 6
8x - 3y = -4
(1, 4)
x - 7y = 18
4x - 14y = 30
(-3, -3)
2(5 – 3x) = -6x – 16
No Solution
Cameron goes to the store with $18 to buy chips and sodas for a party he is having. A bag of chips costs $3 and a soda costs $2. Let c be the number of bags of chips and s be the number of soda cans bought.
3c+2s=18
Determine if the point (2, -5) is a solution to the system of equations. Explain why or why not.
y=2x-9 and -3x-y=-1
It is a solution to the system.
x - 2y = -3
8x - 6y = 16
(5, 4)
-2x + 7y = 4
-5x - 9y = 10
(-2, 0)