Question

50 Points!

Answer 1

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
3x-2y=4 +
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
-4x+14y=-6 +
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
1x-2y=-4 +
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
-120=-3c-3a +
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

Answer 2

Question 1: 
You should know that the Y on both lines will be crossed out and then you add the X which you will end up with: 
4X = 8 
X = 8/4 = 2 

So, y is: 
2 + 2Y = 4 
2Y = 2 
Y = 1 
Answer is: (2,1) 

Question 2: 
what you should do is to solve the second line for Y, then plug the Y in the Y that is in the first line! 
So Y is equal to: Y = 2/7X - 3/7 
Plug it in: 4X - 14( 2/7X - 3/7) = 6 
Solve for X: X= 5/3 
Now solve for Y: Y= 0.2857142857 
(if you out them in the equations you will get 6)

Question 3: 
Same as the Question 2. Solve for Y. then find the number of X. Then find the answer for Y. 
Answer: X= -11/4 and Y= .625 :)

Question 4: 
4X in the first line, then 8X in the second one. So, you can say that their numbers are multiplied by 2. 
So, B is 10 and C is 16. 

Question 5: 
a. T
b. Always. F
c. T
d. never. F

3c + 5a = 150 
a + c = 40 
these two equations can solve the problem! 
Answer: a = 15 and c= 25 :) 

Have a wonderful day! 
(this question took me more than I expected)