Substitution
3x+5y=12
x=4
x=4, y=0
2x-y=11
x+y=7
x=6, y=1
Simplify the following inequality:
-5y-20≤10x
y≥-2x-4
For the following equation, let "x" represent the number of apples and "y" represent the number of oranges.
If you bought two apples, and $3.00x+$4.00y=$14,
How many oranges did you buy?
2 oranges
y=mx+b
What does my slope "m" represent in a graph?
What does the y-intercept "b" represent in a graph?
Various Answers:
m = steepness, rise over run, and it can also tell you in which direction you're going.
b = the point on the graph that the equation INTERSECTS the y-axis
2x+3y=12
x=3
x=3, y=2
x+y=10
x-y=10
x=10, y=0
Simplify the following inequality:
2y+16≤4x
y≤2x-8
Armando goes to the farmer's market and buys a total of 20 fruits and vegetables.
f + v = 20
Jacob also went to the farmer's market, and bought three times as many fruits as Armando. In total, he had 30 fruits and vegetables.
3f + v = 30
How many vegetables did Armando buy?
15 vegetables
Slope-Intercept form is represented by the equation:
y=mx+b
What does "m" represent?
What does "b" represent?
m = slope
b = y-intercept
2x-3y=-1
y=x-1
x=4, y=3
-4x-2y=-12
4x+8y=-24
x=6, y=-6
Simplify the following inequality:
7x - y/7 ≥ 3
y ≤ 49x-21
Mr. Kei is selling tickets for a fundraiser.
He is selling adult tickets and kid tickets.
Let "a" = the price of an adult ticket and
Let "k" = the price of a kid ticket.
Solve for "a" and "k" in the following system of equations:
125a + 30k = 715
100a + 60k = 680
Adult tickets cost $5
Kid tickets cost $3
Given the following equation
y=3x-22
What is the y-intercept, and what (x,y) coordinate point does it represent?
The y-intercept is -22 and it represents the (0,-22) coordinate point.
10x-9y=24
y-x=-2
x=6, y=4
-5y+4x=49
7y+2x=-23
x=6, y=-5
Graph the following inequality:
6x-4y≥16
On TV
Suppose you buy tacos and burritos from a lunch truck.
You buy 3 tacos and 3 burritos for $11.25
Your friend buys 4 tacos and 2 burritos for $10.00
How much does each taco and burrito cost?
(Hint: Make a system of equations)
Each taco costs $1.25 and each burrito costs $2.50
Convert the following equation into slope-intercept form:
1/4y=2x-3
What are your slope and y-intercept?
y=8x-12
Slope = 8
y-intercept "b" = -12
-5x+y=-2
-3x+6y=-12
x=0, y=-2
5x+4y=-30
3x-9y=-18
x=-6, y=0
Graph the inequality:
x/3 - 4y/6 < 6
y > x/2 - 9
Suppose you are comparing gym membership prices. Let "x" represent the number of months and "y" represent the total cost in the following equations:
y = $25x + $45 } Gym A
y = $35x + $5 } Gym B
What do your y-intercepts represent for each Gym?
Which gym is cheaper after 6 months?
What would solving the system of equations tell us?
y-intercept is the Enrollment fee/Sign-up fee
Gym A is cheaper by $20 after 6 months.
Gym A = $195 for 6 months.
Gym B = $215 for 6 months.
The system of equations would tell us when both memberships are equal in total pricing, which is at 4 months.
Convert the following equation into slope-intercept form:
1/3x - 1/4y = 2
Then GRAPH it.
y = 4/3x - 8