Systems of Equations
4x-3y=18
y=-2
(3,-2)
3-x=3-5x
x=0
Solve for w:
A=l*w
w=A/l
n^2+7n+10=0
n= -5 and -2
WRITE AN EQUATION & SOLVE: Trenae is 3 years older than her brother. Trenae's age is 11 years old. How old is her Brother?
n - Trenae's brother's age
n + 3 = 11
n = 8
Trenae's brother is 8 years old.
-3x-2y=-12
y=5x-7
(2,3)
-13(4+2a)=208
a = -10
Solve for x:
u=2x-2
x=(u+2)/2
x^2-10x+22=-2
x=6 and 4
Mr. Liddell bought 7 Hannah Montana t-shirts for a total of $90.93. Each t-shirt cost the same amount. How many Hannah Montana t-shirts did Mr. Liddell buy?
n - # of t-shirts
7n = 90.93
n = 12.99 Each t-shirt cost $12.99
-7x-2y=-13
x-2y=11
(3,-4)
75=3(-6n-5)
n=-5
Solve for a:
z=b+m/a
a=m/(z-b)
6n^2-18n-24=0
n= 4 and -1
Angelo has 4 boxes of apples. Each box has the same number of apples. After Angelo eats 3 apples, there are 109 apples left in the boxes. How many apples were in each box?
a - # of apples in each box
4a - 3 = 109
a = 28 There were 28 apples in each box.
-4x+y=6
-5x-y=21
(-3,-6)
6(6v+6)-5=1+6v
v=-1
Solve for a:
u+ka=ba
a=-u/(k-b)
7h^2-14h=-7
h=1
Camaya goes to the grocery store and purchases 17 bags of raisins and a $2.97 jar of peanut butter. Her total cost was $34.76. What was the cost for a bag of raisins?
r - cost of a bag of raisins
17r + 2.97 = 34.76
r = 1.87 Each bag of raisins cost $1.87
-2x+6y=6
-7x+8y=-5
(3,2)
-10n+3(8+8n)=-6(n-4)
n=0
Solve for x:
4x=-4r+2d
x=(-2r+d)/2
5r^2-44r+120=-30+11r
r = 6 and 5
When you count by ones from many integers, you are counting consecutive integers. Using variables, three consecutive integers are n, n + 1, and n + 2. The sum of three consecutive integers is 48. What are the integers?
n + (n + 1) + (n + 2) = 48
n = 15 The integers are 15, 16, and 17.