Answer:
The system of linear equations that can be used to determine the time that each of the trains has been traveling is:
E + W = 4 ....... Equation 1
95 E + 110W = 400 ......Equation 2
Hence,
An Eastbound train has been travelling for = (E) = 2.67 hours
A Westbound train has been travelling for = (W) = 1.33 hours
Step-by-step explanation:
An Eastbound train (E) traveling 95 mph and a Westbound train (W) traveling 110 mph leave the same train station at different times. After 4 hours, they are 4 00 miles apart. Which system of linear equations can be used to determine the time that each of the trains has been traveling?
Speed = Distance/Time
Distance = Speed × Time
Let the time
An Eastbound train = (E)
A Westbound train = (W)
E + W = 4 hours ....... Equation 1
95mph × E + 110mph × W = 400 miles
95 E + 110W = 400 miles ......Equation 2
The system of linear equations that can be used to determine the time that each of the trains has been traveling is:
E + W = 4 ....... Equation 1
95 E + 110W = 400 ......Equation 2
E = 4 - W
We substitute 4 - W for E in Equation 2
95 (4 - W) + 110W = 400
380 - 95W + 110W = 400
Collect like terms
95W - 110W = 400 - 380
15W = 20
W = 20/15
W = 1.3333333333 hours
≈ 1.33 hours
E = 4 - W
E = 4 - 1.33 hours
E = 2.67 hours
Therefore,
An Eastbound train has been travelling for = (E) = 2.67 hours
A Westbound train has been travelling for = (W) = 1.33 hours
Well, 50 points total given, 25 points per user and 13 bonus for brainliest
anyway
1.
add them equations, the y's will cancel
x+2y=4
<span>3x-2y=4 +</span>
4x+0y=8
4x=8
divide by 4 both sides
x=2
sub back
x+2y=4
2+2y=4
minus 2
2y=2
divide 2
y=1
x=2
y=1
(x,y)
(2,1) is solution
2.
the solution is where they intersect
multiply 2nd equation by 2 and add to first
4x-14y=6
<span>-4x+14y=-6 +</span>
0x+0y=0
0=0
infinite solutions
that is because they are actually the same line
the solutions are (x,y) such that they satisfy -2x+7y=-3 or 4x-14y=6 (same equaiton)
infinite solutions
3.
multiply first equation by 2 and add to first
4x+2y=-6
<span>1x-2y=-4 +</span>
5x+0y=-10
5x=-10
divide by 5 both sides
x=-2
sub bac
x-2y=-4
-2-2y=-4
add 2
-2y=-2
divide by -2
y=1
x=-2
y=1
(x,y)
(-2,1)
4.
coincident means they are the same line
so
we see that we have to multiply 4 by 2 to get 8
multiply top equation by 2
8x+10y=16
8x+By=C
B=10 and C=16
5.
a. false, either 0, 1, or infinity solutions
change the word 'two' to 'one' or 'zero' or 'infinite', or change 'can' into 'can't'
b.false
'sometimes' to 'always'
c. true
d. false, change 'sometimes' to 'always'
EC
total cost=150
TC=childC+adultC
TC=3c+5a
150=3c+5a
40 tickets, c+a
40=c+a
the equations are
150=3c+5a and
40=c+a
eliminate
multiply 2nd equaton by -3 and ad to first one
150=3c+5a
<span>-120=-3c-3a +</span>
30=0c+2a
30=2a
divide by 2
15=a
sub back
40=c+a
40=c+15
minus 15
25=c
25 children tickets and 15 adult tickets were sold
ANSWERS:
1.
(2,1) is solution
2.
infinite solutions
3.
(-2,1)
4.
B=10 and C=16
5.
a. false,
change the word 'two' to 'one' or 'zero' or 'infinite', or change 'can' into 'can't'
b.false
'sometimes' to 'always'
c. true
d. false, change 'sometimes' to 'always'
EC
the equations are
150=3c+5a and
40=c+a
25 children tickets and 15 adult tickets were sold
U can write 3 and one fourth as 325
