Write the linear equation
Nadia swims at a rate of 50 meters per minute. Create a function f, where f(n) gives the number of meters Nadia swims given the number of minutes she swims, n.
f(n)= 50n
6a + 5a = −11
6a + 5a = −11
11a= -11
a=-1
g=6x , for x
g=6x , for x
g/6 = x
Which method would you use (graphing, substitution, or elimination) and WHY!
y = 5x - 2
y = -x + 4
y = 5x - 2
y = -x + 4
GRAPHING, both equations are in slope intercept form
Solve
y = 7x + 15
y = -2x + 6
y = 7x + 15
y = -2x + 6
Graphing (-1,8)
Rod is paid an overtime rate of $25 per hour after his basic wage of $600 per week. Write an equation in slope-intercept form for the total pay p if he works h hour of overtime.
p= 600+25h
4x + 6 + 3 = 17
4x + 6 + 3 = 17
4x+9=17
4x=8
x=2
z=m-x , for x
z=m-x , for x
z-m=-x
-z+m=x
x= -z+m
Which method would you use (graphing, substitution, or elimination) and WHY!
-2x + 4y = -10
y = -6x - 9
-2x + 4y = -10
y = -6x - 9
SUBSTITUTION: One of your equations has the variable (y) already solved for. Just plug in for y and solve
Solve
-2x + 4y = -10
y = -6x - 9
-2x + 4y = -10
y = -6x - 9
Substitution
(-1.-3)
An airplane 30,000 feet above the ground begins descending at the rate of 2000 feet per minute. Assume the plane continues at the same rate of descent. Write an equation to represent the height of the airplane in feet above the ground f(x) in relationship to time in minutes x.
f(x)= 30,000-2000x
42 = 8m + 13m
42 = 8m + 13m
42=21m
21m=42
m=2
u=k/a, for a
u=k/a, for a
ua = k
a = k/u
Which method would you use (graphing, substitution, or elimination) and WHY!
9x + 9y = 11
-9x - 9y = -9
9x + 9y = 11
-9x - 9y = -9
ELIMINATION: You can add the equations together and the x's will cancel out.
Solve
-9x - 9y = 0
6x + 9y = -6
-9x - 9y = 0
6x + 9y = -6
Elimination (2,-2)
A plumber charges a fee of $50 to make a house call. He also charges $25 an hour for labor. Write an equation that you could use to find the amount a plumber charges for a house call based on the number of hours of labor. Let x represent the number of hours for labor and y represent the total cost.
y= 25x+50
18 = 3(3x − 6)
18 = 3(3x − 6)
3(3x-6)=18
9x-18=18
9x=36
x=4
3am = n+p, for m
3am = n+p, for m
m= (n+p)/3a
Which method would you use (graphing, substitution, or elimination) and WHY!
4x - y = -5
y = 4x + 5
4x - y = -5
y = 4x + 5
SUBSTITUTION: One of your equations has the variable (y) already solved for. Just plug in for y and solve
4x + 2y = -22
4x + 10y = -30
4x + 2y = -22
4x + 10y = -30
Elimination (-5,-1)
Suppose you receive $100 for a graduation present, and you deposit it in a savings account. Then each week thereafter, you add $5 to the account but no interest is earned. The amount in the account is a function of the number of weeks that have passed.
100+5x
−13 = 5(1 + 4m) − 2m
−13 = 5(1 + 4m) − 2m
5(1 + 4m) - 2m = -13
5 + 20m - 2m = -13
5 + 18m = -13
18m = -18
m= -1
u= ak/b, for a
u= ak/b, for a
ub= ak
ak = ub
a = ub/k
Which method would you use (graphing, substitution, or elimination) and WHY!
4x + 2y = -22
4x + 10y = -30
4x + 2y = -22
4x + 10y = -30
ELIMINATION: Multiply either the top or bottom equation by -1. Then, you can add the equations together and the x's will cancel out.
Solve
9x + 9y = 11
-9x - 9y = -9
9x + 9y = 11
-9x - 9y = -9
Elimination
No solution