smithm29:
solving problems with linear systems
Vocaloid:
airplane speed - wind = 2460/4 airplane speed + wind = 2460/5 add the equations together and solve for airplane speed
smithm29:
553.5?
Vocaloid:
good
smithm29:
is that the answer?
Vocaloid:
yes
Vocaloid:
I'm thinking, please be patient...
smithm29:
sorry
Vocaloid:
if we let small van = x and big van = x + 5 then each morning we have 2x + x + 5 = 65 solve for x
smithm29:
x=20?
Vocaloid:
good, so big bus = x + 5 = ?
smithm29:
25
smithm29:
is the answer?
Vocaloid:
read the question again. you tell me.
smithm29:
sorry i just wanna make sure im right bc i make MANY mistakes
Vocaloid:
good, let's keep going
smithm29:
k
Vocaloid:
x + y has to be less than/equal to 150 (maximum load) the 2000x + 1500y < = 175,000 (maximum letters)
Vocaloid:
cost has to be <= 200 bratwurst + burgers >= 150
Vocaloid:
if y = the more expensive tree then y >= x budget needs to be <= 56000
smithm29:
should we do the cancel out one?
Vocaloid:
yeah, start by subtracting the equations
smithm29:
x=6?
smithm29:
y=19.7?
Vocaloid:
check your math
Vocaloid:
-17x - 12x = ?
smithm29:
-29x
Vocaloid:
good -95 - 50 = ?
smithm29:
-145
Vocaloid:
good so if -29x = -145 x = ?
smithm29:
5
Vocaloid:
good, now we go back 12(5) = 50 - 10y y = ?
smithm29:
-1?
Vocaloid:
good so (5,-1) = your ans
Vocaloid:
same process, subtract the two equations make sure you are subtracting the x's, then subtracting the whole numbers
smithm29:
-2
Vocaloid:
good, now let's find y 8(-2) = 84 - 20y
smithm29:
5?
Vocaloid:
good, so -2,5 = ans
Vocaloid:
add the equations together
smithm29:
-1?
Vocaloid:
good, now let's find y 1 = 29 - 14y y = ?
smithm29:
2?
Vocaloid:
good so (-1,2)
Vocaloid:
add them together and solve for x
smithm29:
4
Vocaloid:
good so 5(4) = 8 + 6y y = ?
smithm29:
2
Vocaloid:
good, so (4,2) = your answer
smithm29:
do i add or subtract this one?
Vocaloid:
first multiply the second equation by 2 then subtract and solve for y
Vocaloid:
to determine whether to add/subtract the equation, look at what you are trying to eliminate
Vocaloid:
since we are trying to eliminate the x's, and the x's are both positive, we subtract
smithm29:
um i got -10.2
Vocaloid:
so we have: 14x + 11y = 23 14x - 6y = 74
Vocaloid:
subtract 11y - (-6y) = ?
smithm29:
17y
Vocaloid:
good. 23 - 74 = ?
smithm29:
-51
Vocaloid:
good, so if 17y = -51 then y = ?
smithm29:
-3
smithm29:
?
smithm29:
am i right?*
Vocaloid:
yes good
Vocaloid:
now re-subsbtitute to find x
smithm29:
4?
Vocaloid:
good, so (4,-3)
Vocaloid:
double the first equation and subtract to find y
smithm29:
-4?
smithm29:
nvm i messed up hold on
smithm29:
y=-5?
Vocaloid:
yes, y = -5 is good
smithm29:
sweet
Vocaloid:
6x + 5(-5) = -19 x = ?
smithm29:
1
Vocaloid:
good, so 1,-5
Vocaloid:
how many are left? I need to go to sleep soon
smithm29:
ik same um... 2 more
smithm29:
is that ok?
Vocaloid:
ok
Vocaloid:
double first equation then subtract to find y
smithm29:
i dont thik this is right
smithm29:
14.6repeated
Vocaloid:
16x - 8y = -16 16x - 5y = -28 subtract the y's, subtract the whole numbers, then solve for y
Vocaloid:
take it slowly
smithm29:
16x-8y=-16 16x-5y=-28 -3y=-44 /(-3) /(-3) y=14.666 what am i doin wrong?
Vocaloid:
-16 - (-28) is not -44
smithm29:
oh i mustve typed it wrong
Vocaloid:
-16 - (-28) = 12
Vocaloid:
so -3y = 12 and y = -4
smithm29:
yeah i got that now lol
smithm29:
ok soo now plug in y right?
Vocaloid:
yep
Vocaloid:
16x-8(-4 )= -16 x = ?
smithm29:
-3?
Vocaloid:
one more time
smithm29:
never mind i did *8 instead of -16
smithm29:
-8*
smithm29:
-3?
Vocaloid:
good so (-3,-4)
smithm29:
this is the last one
Vocaloid:
multiply the first equation by 7 and the second equation by 2
Vocaloid:
14x + 14y = -56 -26x + 14y = -96 then subtract to find x
smithm29:
x=1?
Vocaloid:
good
Vocaloid:
14(1) + 14y = -56 y = ?
smithm29:
-5?
Vocaloid:
good, so 1,-5
smithm29:
ok thank u so much and gn
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