Question

Choose the point which is a solution to the system of inequalities:

2x - 3y greater than or equal to 12
x + y less than or equal to 7

(-9, -1)
(3, -6)
(12, -3)
(6, 9)


Two boats leave from the same dock traveling in opposite directions. The first boat is traveling 25 mph and the second is traveling 29 mph. How long will it take before they are 162 miles apart?

1 hour
2 hours
3 hours
4 hours

Answer 1

Are those points the one that came with the question?

Answer 2

do u know how to solve simultaneous equations?

Answer 3

2x - 3y >= 12
x + y <= 7

Answer 4

multiply both sides of the 2nd equation by -2 and add the 2 equations , know how to do this?

Answer 5

im really confused on how to even do these questions. kx2bay

Answer 6

just try , I gave you the first step above, do you know how to multiply ?

Answer 7

-2(x + y) >= -2*7 .... notice when multitplying by -2 the sign <= changed to >=
-2x - 2y >= -14

Answer 8

now add the 2 equations
2x - 3y >= 12
-2x - 2y >= -14
==========
you get -5y >= -2
now divide by -5 both sides (the inequality sign will change)
you'll get y <= 2/5
********************
now can you find x ?

Answer 9

Oh wow, makes sense now! we eliminated the x and we got y so now we plug the y into one of the equations to get x right?

Answer 10

yep, can you do that?

Answer 11

let y = 2/5 and substitute it in either of the 2 equations, perhaps use the shorter one
x + y <= 7

what will x be then?

Answer 12

x = -2/5 + 7 is what i got, i cant think of anything else to do to it.

Answer 13

x <= 33/5

Answer 14

so now you have both x and y
x <= 33/5 , and
y <= 2/5

and if you said x = 33/5 and y = 2/5 and substituted these values in any of the 2 equations you'll get the equation 1 is equal to 12 and equation 2 is equal to 7

Answer 15

the answer is (-9, -1)

Answer 16

with the second question about the boats... are you there?

Answer 17

do you understand what it says?

Answer 18

the formula for speed is
speed = distance / time

Answer 19

one boat travels left and passes x miles after some time let's call it "t"
the other boat travels right and passes a different distance y for the same time "t"

Answer 20

it is given that the distance between the 2 boats after the time "t" is 162 miles
so, your first equation is
x + y = 162
now using the law of speed can you make the second formula ?

Answer 21

25 = x / t, or
t = x / 25

and for the other boat
29 = y / t
or
t = y / 29

so...
x / 25 = y / 29

cross multiply , find x in terms of y and substitute in the first formula above, then solve for the other boat

Answer 22

got it????

Answer 23

x = 75 miles
and
y = 87 miles

now using one of the TIME formulas above, find "t" in hours?

use t = x/25 , you know x from above, what is t ?

Answer 24

ok... good luck sandy :)