Multi-Step Review
Solve:
14 + 4v = 7v - 1
y = 3x + 6
y = 2.5x - 5
One Solution
Solve the following system of equation:
y = 5x - 2
y = 6x
(-2, -12)
Is (2, 8) a solution to the following system?
y = 12x + 3
y = x - 8
Nope! When you plug (2, 8) into the equation y = x - 8, you get 8 = -6.
House Painting Inc. charges $500 to show up to a job, and then $100 per hour. Get Ur Houz Painted charges $100 to show up, and then $150 per hour.
Write the equations for both companies.
House Painting Inc.: Cost = 100h + 500
Get Ur Houz Painted: Cost = 150h + 100
5n + 4n = 6n + n
n = 0
y = -2x - 4
y = -2x + 8
No Solutions
Solve the following system of equation:
y = 2x - 3
y = 2x + 1
No Solution
Is (1, -5) a solution to the following system?
y = -10x + 5
y = -x - 4
Yes, when it is put in to the equations, you get:
-5 = -5
Brooke's Bakery does catering. She charges $50 per event, plus $10 per person who attends. Camille's Cookies charges $100 per event, and $7.50 per person who attends.
If you were to solve this as a system of equation, what would the solution tell you in real life?
It would tell us at what number of people at the event both Brooke's Bakery and Camille's Cookies cost the same amount.
2 (1 + 4x) = -31 - 3x
x = -3
y= 3x + 5
y = 3x + 5
Infinite Solutions
Solve the following system of equation:
y = -x + 2
y = x + 6
(-2, 4)
Is (-2, -1) a solution to the system:
y = 3x + 5
y = -3x - 7
Yes, when put into the equations, you get:
- 1 = -1
Aero's Aeronautics builds planes. They charge $30,000 as a deposit, then $100,000 per plane. Hawn's Helicopters charges a deposit of $90,000 and $80,000 per helicopter.
Which business is cheaper to build 4 aircraft? How much will they cost?
4 (m - 8) = -26 + 5m
m = -6
y = -4x + 5
y = -4x + 2
No Solution
Solve the following system of equation:
y = x + 5
y = 4x - 1
(2, 7)
Is (3, 4) a solution to the system:
y = 10x - 2
y = x + 7
No, when you plug it into the equation y = 10x - 2, you get 4 = 28.
Jesse and Jace are juggling two judicious jobs. Jesse works as an engineer designing homes. He charges $4000 per house and then $200 per hour as his fee. Jace is a thriving artist, charging $1000 per painting, plus $500 per hour as his fee.
At how many hours of work will they make the same amount? How much will they make?
10 hours, $6,000 each
Solve:
2 ( 3v + 4) = 7 (v - 2) - 3v
v = -11
6x + 2y = 4
-4x + 4y = 12
One Solution: When manipulated, the equations turn in to:
y = 2 - 3x
y = 3 + x
y = -7
y = 6x - 1
(-1, -7)
Is (-2, 5) a solution to the system:
y = -5x - 5
y = 1.5x + 8
Yes, when you plug it into both equations, you get 5 = 5.